Reference Encyclopedia of Optimization

Z......Page 0
ABS Algorithms for Linear Equations and Linear Least Squares......Page 1
ABS Algorithms for Optimization......Page 7
Adaptive Convexification in Semi-Infinite Optimization......Page 14
Adaptive Global Search......Page 19
Adaptive Simulated Annealing and its Application to Protein Folding......Page 21
Airline Optimization......Page 26
Algorithmic Improvements Using a Heuristic Parameter, Reject Index for Interval Optimization......Page 30
Algorithms for Genomic Analysis......Page 33
Alignment Problem......Page 54
αBB Algorithm......Page 61
Alternative Set Theory......Page 73
Approximation of Extremum Problems with Probability Functionals......Page 78
Approximation ofMultivariate Probability Integrals......Page 83
Approximations to Robust Conic Optimization Problems......Page 90
Archimedes and the Foundations of Industrial Engineering......Page 96
Asset Liability Management Decision Support System......Page 98
Assignment andMatching......Page 106
Assignment Methods in Clustering......Page 108
Asymptotic Properties of Random Multidimensional Assignment Problem......Page 114
Asynchronous Distributed Optimization Algorithms......Page 123
Auction Algorithms......Page 128
Automatic Differentiation: Calculation of the Hessian......Page 133
Automatic Differentiation: Calculation of Newton Steps......Page 137
Automatic Differentiation: Geometry of Satellites and Tracking Stations......Page 142
Automatic Differentiation: Introduction, History and Rounding Error Estimation......Page 153
Automatic Differentiation: Parallel Computation......Page 159
Automatic Differentiation: Point and Interval......Page 165
Automatic Differentiation: Point and Interval Taylor Operators......Page 171
Automatic Differentiation: Root Problemand Branch Problem......Page 176
Bayesian Global Optimization......Page 182
Bayesian Networks......Page 186
Beam Selection in Radiotherapy Treatment Design......Page 195
Best Approximation in Ordered Normed Linear Spaces......Page 201
Bilevel Fractional Programming......Page 218
Bilevel Linear Programming......Page 220
Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs......Page 224
Bilevel Optimization: Feasibility Test and Flexibility Index......Page 227
Bilevel Programming......Page 238
Bilevel Programming: Applications......Page 240
Bilevel Programming: Applications in Engineering......Page 242
Bilevel Programming Framework for Enterprise-Wide Process Networks Under Uncertainty......Page 247
Bilevel Programming: Global Optimization......Page 254
Bilevel Programming: Implicit Function Approach......Page 259
Bilevel Programming: Introduction, History and Overview......Page 265
Bilevel Programming in Management......Page 268
Bilevel Programming: Optimality Conditions and Duality......Page 273
Bilinear Programming......Page 278
Bilinear Programming: Applications in the Supply Chain Management......Page 281
Bi-Objective Assignment Problem......Page 287
Biquadratic Assignment Problem......Page 292
Bisection Global Optimization Methods......Page 293
Boolean and Fuzzy Relations......Page 296
Bottleneck Steiner Tree Problems......Page 310
Boundary Condition Iteration BCI......Page 312
Bounding Derivative Ranges......Page 317
Bounds and Solution Vector Estimates for Parametric NLPS......Page 324
Branch and Price: Integer Programming with Column Generation......Page 327
Branchwidth and Branch Decompositions1......Page 331
Broadcast Scheduling Problem......Page 338
Broyden Family ofMethods and the BFGS Update......Page 344
CapacitatedMinimum Spanning Trees......Page 346
Carathéodory, Constantine......Page 356
Carathéodory Theorem......Page 357
Checklist Paradigm Semantics for Fuzzy Logics......Page 358
Chemical Process Planning......Page 368
Cholesky Factorization......Page 373
CombinatorialMatrix Analysis......Page 376
Combinatorial Optimization Algorithms in Resource Allocation Problems......Page 381
Combinatorial Optimization Games......Page 386
Combinatorial Test Problems and Problem Generators......Page 390
Communication Network Assignment Problem......Page 393
Competitive Facility Location......Page 395
Competitive Ratio for Portfolio Management......Page 400
Complementarity Algorithms in Pattern Recognition......Page 404
Complexity Classes in Optimization......Page 412
Complexity of Degeneracy......Page 418
Complexity of Gradients, Jacobians, and Hessians......Page 424
Complexity and Large-Scale Least Squares Problems......Page 434
Complexity Theory......Page 446
Complexity Theory: Quadratic Programming......Page 450
Composite Nonsmooth Optimization......Page 453
Computational Complexity Theory......Page 456
Concave Programming......Page 461
Conjugate-Gradient Methods......Page 465
ContactMap OverlapMaximization Problem, CMO......Page 470
Continuous Approximations to Subdifferentials......Page 474
Continuous Global Optimization: Applications......Page 481
Continuous Global Optimization: Models, Algorithms and Software......Page 485
Continuous Reformulations of Discrete-Continuous Optimization Problems......Page 492
Continuous Review Inventory Models: (Q, R) Policy......Page 500
Contraction-Mapping......Page 504
Control Vector Iteration CVI......Page 508
Convex Discrete Optimization......Page 512
Convex Envelopes in Optimization Problems......Page 549
Convexifiable Functions, Characterization of1......Page 550
Convex Max-Functions......Page 554
Convex-Simplex Algorithm......Page 557
Copositive Optimization......Page 560
Copositive Programming......Page 563
Cost Approximation Algorithms......Page 566
Credit Rating and OptimizationMethods......Page 577
Criss-Cross Pivoting Rules......Page 583
Cutting PlaneMethods for Global Optimization......Page 589
Cutting-Stock Problem......Page 593
Cyclic Coordinate Method......Page 594
Data Envelopment Analysis......Page 596
Data Mining......Page 599
D.C. Programming......Page 606
Decision Support Systems withMultiple Criteria......Page 611
Decomposition Algorithms for the Solution of Multistage Mean-Variance Optimization Problems......Page 618
Decomposition in Global Optimization......Page 626
Decomposition Principle of Linear Programming......Page 629
Decomposition Techniques forMILP: Lagrangian Relaxation......Page 631
De Novo Protein Design Using Flexible Templates......Page 637
De Novo Protein Design Using Rigid Templates......Page 642
Derivative-FreeMethods for Non-smooth Optimization......Page 647
Derivatives ofMarkov Processes and Their Simulation......Page 654
Derivatives of Probability and Integral Functions: General Theory and Examples......Page 657
Derivatives of Probability Measures......Page 663
Design Optimization in Computational Fluid Dynamics......Page 665
Design of Robust Model-Based Controllers via Parametric Programming......Page 676
Determining the Optimal Number of Clusters......Page 686
Deterministic and Probabilistic OptimizationModels for Data Classification......Page 693
Differential Equations and Global Optimization......Page 701
Dini and Hadamard Derivatives in Optimization......Page 709
Directed Tree Networks......Page 715
Direct Global Optimization Algorithm......Page 724
Direct Search Luus–Jaakola Optimization Procedure......Page 734
Discontinuous Optimization......Page 738
Discretely Distributed Stochastic Programs: Descent Directions and Efficient Points......Page 743
Discrete Stochastic Optimization......Page 750
Disease Diagnosis: Optimization-BasedMethods......Page 752
Disjunctive Programming......Page 783
Distance Dependent Protein Force Field via Linear Optimization......Page 786
Domination Analysis in Combinatorial Optimization......Page 791
Duality Gaps in Nonconvex Optimization......Page 801
Duality in Optimal Control with First Order Differential Equations......Page 804
Duality for Semidefinite Programming......Page 810
Duality Theory: Biduality in Nonconvex Optimization......Page 813
Duality Theory: Monoduality in Convex Optimization......Page 817
Duality Theory: Triduality in Global Optimization......Page 821
Dykstra’s Algorithm and Robust Stopping Criteria......Page 827
Dynamic Programming: Average Cost Per Stage Problems......Page 832
Dynamic Programming in Clustering......Page 836
Dynamic Programming: Continuous-time Optimal Control......Page 843
Dynamic Programming: Discounted Problems......Page 845
Dynamic Programming: Infinite Horizon Problems, Overview......Page 849
Dynamic Programming: Inventory Control......Page 852
Dynamic Programming and Newton’sMethod in Unconstrained Optimal Control......Page 855
Dynamic Programming: Optimal Control Applications......Page 861
Dynamic Programming: Stochastic Shortest Path Problems......Page 868
Dynamic Programming: Undiscounted Problems......Page 872
Dynamic Traffic Networks......Page 875
Economic Lot-Sizing Problem......Page 882
Eigenvalue Enclosures for Ordinary Differential Equations......Page 886
EllipsoidMethod......Page 889
Emergency Evacuation, OptimizationModeling......Page 899
Entropy Optimization: Interior PointMethods......Page 906
Entropy Optimization: Parameter Estimation......Page 911
Entropy Optimization: ShannonMeasure of Entropy and its Properties......Page 915
Equality-Constrained Nonlinear Programming: KKT Necessary Optimality Conditions......Page 920
Equilibrium Networks......Page 922
Equivalence Between Nonlinear Complementarity Problem and Fixed Point Problem......Page 926
Estimating Data forMulticriteria Decision Making Problems: Optimization Techniques......Page 930
Evacuation Networks......Page 939
Evolutionary Algorithms in Combinatorial Optimization......Page 949
Extended Cutting Plane Algorithm......Page 958
Extension of the Fundamental Theorem of Linear Programming......Page 965
Extremum Problems with Probability Functions: Kernel Type Solution Methods......Page 968
Facilities Layout Problems......Page 973
Facility Location with Externalities......Page 977
Facility Location Problems with Spatial Interaction......Page 980
Facility Location with Staircase Costs......Page 987
Farkas Lemma......Page 993
Farkas Lemma: Generalizations......Page 996
Feasible Sequential Quadratic Programming......Page 999
Feedback Set Problems......Page 1003
FejérMonotonicity in Convex Optimization......Page 1014
Financial Applications of Multicriteria Analysis......Page 1022
Financial Equilibrium......Page 1033
Financial Optimization......Page 1038
Finite Complete Systems of Many-valued Logic Algebras......Page 1046
First Order Constraint Qualifications......Page 1053
Flow Shop Scheduling Problem......Page 1058
Forecasting......Page 1066
Fourier–Motzkin EliminationMethod......Page 1072
Fractional Combinatorial Optimization......Page 1075
Fractional Programming......Page 1078
Fractional Zero-One Programming......Page 1089
Frank–Wolfe Algorithm......Page 1092
Frequency Assignment Problem......Page 1095
Fundamental Theorem of Algebra......Page 1099
FuzzyMulti-objective Linear Programming......Page 1101
Gasoline Blending and Distribution Scheduling: AnMILPModel......Page 1111
Gauss, Carl Friedrich......Page 1125
Gauss–NewtonMethod: Least Squares, Relation to Newton’s Method......Page 1127
Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning......Page 1132
Generalizations of Interior Point Methods for the Linear Complementarity Problem......Page 1143
Generalized Assignment Problem......Page 1151
Generalized Benders Decomposition......Page 1160
Generalized Concavity inMulti-objective Optimization......Page 1173
Generalized Disjunctive Programming......Page 1178
Generalized Eigenvalue Proximal Support VectorMachine Problem......Page 1181
Generalized Geometric Programming: Mixed Continuous and Discrete Free Variables......Page 1183
GeneralizedMonotone MultivaluedMaps......Page 1191
GeneralizedMonotone Single ValuedMaps......Page 1195
GeneralizedMonotonicity: Applications to Variational Inequalities and Equilibrium Problems......Page 1200
Generalized Networks......Page 1207
Generalized Nonlinear Complementarity Problem......Page 1212
Generalized Outer Approximation......Page 1213
Generalized Primal-relaxed Dual Approach......Page 1221
Generalized Semi-infinite Programming: Optimality Conditions......Page 1225
Generalized Total Least Squares......Page 1231
Generalized Variational Inequalities: A Brief Review......Page 1236
GeneralMoment Optimization Problems......Page 1242
General Routing Problem......Page 1250
Genetic Algorithms......Page 1252
Genetic Algorithms for Protein Structure Prediction......Page 1255
Geometric Programming......Page 1258
Global Equilibrium Search......Page 1266
Globally Convergent HomotopyMethods......Page 1270
Global Optimization Algorithms for Financial Planning Problems......Page 1275
Global Optimization in the Analysis and Management of Environmental Systems......Page 1280
Global Optimization: Application to Phase Equilibrium Problems......Page 1284
Global Optimization Based on StatisticalModels......Page 1289
Global Optimization in Batch Design Under Uncertainty......Page 1292
Global Optimization in Binary Star Astronomy......Page 1297
Global Optimization: Cutting AngleMethod......Page 1302
Global Optimization: Envelope Representation......Page 1309
Global Optimization: Filled FunctionMethods......Page 1314
Global Optimization: Functional Forms......Page 1321
Global Optimization: g- ˛ BB Approach......Page 1326
Global Optimization in Generalized Geometric Programming......Page 1331
Global Optimization of Heat Exchanger Networks......Page 1335
Global Optimization: Hit and RunMethods......Page 1340
Global Optimization: Interval Analysis and Balanced Interval Arithmetic......Page 1344
Global Optimization in Lennard–Jones andMorse Clusters......Page 1348
Global Optimization in Location Problems......Page 1352
Global OptimizationMethods for Harmonic Retrieval......Page 1357
Global OptimizationMethods for Systems of Nonlinear Equations......Page 1362
Global Optimization inMultiplicative Programming......Page 1364
Global Optimization: p- ˛ BB Approach......Page 1368
Global Optimization in Phase and Chemical Reaction Equilibrium......Page 1374
Global Optimization of Planar Multilayered Dielectric Structures......Page 1381
Global Optimization in Protein Folding......Page 1390
Global Optimization: Tight Convex Underestimators......Page 1409
Global Optimization Using Space Filling......Page 1416
Global Optimization in Weber’s Problem with Attraction and Repulsion......Page 1421
Global Pairwise Protein Sequence Alignment viaMixed-Integer Linear Optimization......Page 1425
Global Supply ChainModels......Page 1432
Global TerrainMethods......Page 1435
Graph Coloring......Page 1442
Graph Planarization......Page 1446
Graph Realization via Semidefinite Programming......Page 1451
Greedy Randomized Adaptive Search Procedures......Page 1458
Gröbner Bases for Polynomial Equations......Page 1467
Hamilton–Jacobi–Bellman Equation......Page 1470
Hemivariational Inequalities: Applications inMechanics......Page 1474
Hemivariational Inequalities: Eigenvalue Problems......Page 1480
Hemivariational Inequalities: Static Problems......Page 1485
Heuristic andMetaheuristic Algorithms for the Traveling Salesman Problem......Page 1496
Heuristic Search......Page 1503
Heuristics forMaximum Clique and Independent Set......Page 1505
High-order Maximum Principle for Abnormal Extremals......Page 1517
High-order Necessary Conditions for Optimality for Abnormal Points......Page 1524
Hilbert’s Thirteenth Problem......Page 1532
History of Optimization......Page 1535
Homogeneous SelfdualMethods for Linear Programming......Page 1539
Hyperplane Arrangements......Page 1542
Hyperplane Arrangements in Optimization......Page 1544
IdentificationMethods for Reaction Kinetics and Transport......Page 1546
Ill-posed Variational Problems......Page 1553
Image Space Approach to Optimization......Page 1558
Implicit Lagrangian......Page 1564
Increasing and Convex-Along-Rays Functions on Topological Vector Spaces......Page 1568
Increasing and Positively Homogeneous Functions on Topological Vector Spaces......Page 1573
Inequality-constrained Nonlinear Optimization......Page 1583
Inference ofMonotone Boolean Functions......Page 1588
Infinite Horizon Control and Dynamic Games......Page 1595
Information-based Complexity and Information-based Optimization......Page 1600
Integer Linear Complementary Problem......Page 1605
Integer Linear Programs for Routing and Protection Problems in Optical Networks......Page 1607
Integer Programming......Page 1614
Integer Programming: AlgebraicMethods......Page 1621
Integer Programming: Branch and Bound Methods......Page 1631
Integer Programming: Branch and Cut Algorithms......Page 1640
Integer Programming: Cutting Plane Algorithms......Page 1647
Integer Programming Duality......Page 1654
Integer Programming: Lagrangian Relaxation......Page 1664
Integrated Planning and Scheduling......Page 1670
Interior PointMethods for Semidefinite Programming......Page 1676
Interval Analysis: Application to Chemical Engineering Design Problems......Page 1680
Interval Analysis: Differential Equations......Page 1683
Interval Analysis: Eigenvalue Bounds of IntervalMatrices......Page 1686
Interval Analysis: Intermediate Terms......Page 1693
Interval Analysis: Nondifferentiable Problems......Page 1696
Interval Analysis for Optimization of Dynamical Systems......Page 1699
Interval Analysis: ParallelMethods for Global Optimization......Page 1706
Interval Analysis: Subdivision Directions in Interval Branch and Bound Methods......Page 1714
Interval Analysis: Systems of Nonlinear Equations......Page 1718
Interval Analysis: Unconstrained and Constrained Optimization......Page 1724
Interval Analysis: Verifying Feasibility......Page 1727
Interval Constraints......Page 1730
Interval Fixed Point Theory......Page 1733
Interval Global Optimization......Page 1736
Interval Linear Systems......Page 1754
Interval NewtonMethods......Page 1760
InventoryManagement in Supply Chains......Page 1763
Invexity and its Applications......Page 1767
Isotonic Regression Problems......Page 1771
Jaynes’ Maximum Entropy Principle......Page 1775
Job-shop Scheduling Problem......Page 1778
Kantorovich, Leonid Vitalyevich......Page 1785
Kolmogorov Complexity......Page 1786
Kuhn–Tucker Optimality Conditions......Page 1790
Lagrange, Joseph-Louis......Page 1794
Lagrange-Type Functions......Page 1795
Lagrangian Duality: BASICS......Page 1800
Lagrangian MultipliersMethods for Convex Programming......Page 1808
LaplaceMethod and Applications to Optimization Problems......Page 1813
Large Scale Trust Region Problems......Page 1817
Large Scale Unconstrained Optimization......Page 1826
L-convex Functions andM-convex Functions......Page 1833
LCP: Pardalos–Rosen Mixed Integer Formulation......Page 1840
Least-index Anticycling Rules......Page 1842
Least Squares Orthogonal Polynomials......Page 1846
Least Squares Problems......Page 1851
Leibniz, Gottfried Wilhelm......Page 1861
LemkeMethod......Page 1863
Lexicographic Pivoting Rules......Page 1865
Linear Complementarity Problem......Page 1869
Linear Optimization: Theorems of the Alternative......Page 1873
Linear Ordering Problem......Page 1876
Linear Programming......Page 1878
Linear Programming: Interior PointMethods......Page 1881
Linear Programming: Karmarkar Projective Algorithm......Page 1884
Linear Programming: Klee–Minty Examples......Page 1886
Linear Programming Models for Classification......Page 1892
Linear Space......Page 1896
Lipschitzian Operators in Best Approximation by Bounded or Continuous Functions......Page 1897
Load Balancing for Parallel Optimization Techniques......Page 1900
Local Attractors for Gradient-related Descent Iterations......Page 1906
Location Routing Problem......Page 1914
Logconcave Measures, Logconvexity......Page 1920
Logconcavity of Discrete Distributions......Page 1922
Logic-Based Outer Approximation......Page 1923
Lovász Number......Page 1927
LP Strategy for Interval-Newton Method in Deterministic Global Optimization......Page 1932
L-shapedMethod for Two-stage Stochastic Programs with Recourse......Page 1938
Maritime Inventory Routing Problems......Page 1941
Mathematical Programming for DataMining......Page 1949
Mathematical Programming Methods in Supply Chain Management......Page 1953
Matrix Completion Problems......Page 1961
Matroids......Page 1969
Maximum Constraint Satisfaction: Relaxations and Upper Bounds......Page 1975
Maximum Cut Problem, MAX-CUT......Page 1985
Maximum Entropy and Game Theory......Page 1993
Maximum Entropy Principle: Image Reconstruction......Page 1998
Maximum Flow Problem......Page 2003
Maximum Likelihood Detection via Semidefinite Programming......Page 2014
Maximum PartitionMatching......Page 2023
Maximum Satisfiability Problem......Page 2029
Medium-Term Scheduling of Batch Processes......Page 2035
Metaheuristic Algorithms for the Vehicle Routing Problem......Page 2049
Metaheuristics......Page 2055
Minimax: Directional Differentiability......Page 2069
Minimax Game Tree Searching......Page 2073
Minimax Theorems......Page 2081
Minimum Concave Transportation Problems......Page 2087
Minimum Cost Flow Problem......Page 2089
MINLP: Application in Facility Location-allocation......Page 2102
MINLP: Applications in Blending and Pooling Problems......Page 2108
MINLP: Applications in the Interaction of Design and Control......Page 2115
MINLP: Branch and Bound Global Optimization Algorithm......Page 2126
MINLP: Branch and Bound Methods......Page 2132
MINLP: Design and Scheduling of Batch Processes......Page 2136
MINLP: Generalized Cross Decomposition......Page 2142
MINLP: Global Optimization with ˛ BB......Page 2149
MINLP: Heat Exchanger Network Synthesis......Page 2157
MINLP: Logic-basedMethods......Page 2164
MINLP: Mass and Heat Exchanger Networks......Page 2167
MINLP: Outer Approximation Algorithm......Page 2173
MINLP: Reactive Distillation Column Synthesis......Page 2177
MINLP: Trim-loss Problem......Page 2184
Mixed 0-1 Linear Programming Approach for DNA Transcription Element Identification......Page 2193
Mixed Integer Classification Problems......Page 2204
Mixed Integer Linear Programming: Heat Exchanger Network Synthesis......Page 2208
Mixed Integer Linear Programming: Mass and Heat Exchanger Networks......Page 2211
Mixed Integer Nonlinear Bilevel Programming: Deterministic Global Optimization......Page 2219
Mixed-Integer Nonlinear Optimization: A Disjunctive Cutting Plane Approach......Page 2224
Mixed Integer Nonlinear Programming......Page 2228
Mixed Integer Optimization in Well Scheduling......Page 2241
Mixed Integer Programming/Constraint Programming Hybrid Methods......Page 2264
Model Based Control for Drug Delivery Systems......Page 2270
Modeling Difficult Optimization Problems......Page 2278
Modeling Languages in Optimization: A New Paradigm......Page 2291
Molecular Distance Geometry Problem......Page 2299
Molecular Structure Determination: Convex Global Underestimation......Page 2305
Monotonic Optimization......Page 2310
Monte-Carlo Simulated Annealing in Protein Folding......Page 2317
Monte-Carlo Simulations for Stochastic Optimization......Page 2331
Motzkin Transposition Theorem......Page 2339
Multi-Class Data Classification viaMixed-Integer Optimization......Page 2342
Multicommodity Flow Problems......Page 2348
Multicriteria Decision Support Methodologies for Auditing Decisions......Page 2356
MulticriteriaMethods forMergers and Acquisitions......Page 2366
Multicriteria SortingMethods......Page 2373
Multidimensional Assignment Problem......Page 2390
Multidimensional Knapsack Problems......Page 2396
MultidisciplinaryDesign Optimization......Page 2400
Multifacility and Restricted Location Problems......Page 2403
Multi-index Transportation Problems......Page 2407
Multilevel Methods for Optimal Design......Page 2413
Multilevel Optimization in Mechanics......Page 2422
Multi-objective Combinatorial Optimization......Page 2431
Multi-objective Fractional Programming Problems......Page 2436
Multi-objective Integer Linear Programming......Page 2442
Multi-objectiveMixed Integer Programming......Page 2448
Multi-objective Optimization and Decision Support Systems......Page 2454
Multi-objective Optimization: Interaction of Design and Control......Page 2459
Multi-objectiveOptimization: InteractiveMethods for Preference Value Functions......Page 2465
Multi-objective Optimization: Lagrange Duality......Page 2468
Multi-objective Optimization: Pareto Optimal Solutions, Properties......Page 2472
Multiparametric Linear Programming......Page 2476
MultiparametricMixed Integer Linear Programming......Page 2478
MultipleMinima Problem in Protein Folding: ˛ BB Global Optimization Approach......Page 2484
Multiple Objective Dynamic Programming......Page 2491
Multiple Objective Programming Support......Page 2497
Multiplicative Programming......Page 2505
Multi-Quadratic Integer Programming: Models and Applications......Page 2507
Multi-Scale Global Optimization Using Terrain/Funneling Methods......Page 2514
Multistage Stochastic Programming: Barycentric Approximation......Page 2521
Nested Partitions Optimization......Page 2526
Network Design Problems......Page 2532
Network Location: Covering Problems......Page 2538
Neural Networks for Combinatorial Optimization......Page 2540
Neuro-Dynamic Programming......Page 2548
New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization......Page 2553
Nonconvex Energy Functions: Hemivariational Inequalities......Page 2564
Nonconvex Network Flow Problems......Page 2571
Nonconvex-nonsmooth Calculus of Variations......Page 2574
Nondifferentiable Optimization......Page 2577
Nondifferentiable Optimization: Cutting PlaneMethods......Page 2583
Nondifferentiable Optimization: Minimax Problems......Page 2588
Nondifferentiable Optimization: Newton Method......Page 2595
Nondifferentiable Optimization: Parametric Programming......Page 2600
Nondifferentiable Optimization: RelaxationMethods......Page 2608
Nondifferentiable Optimization: Subgradient OptimizationMethods......Page 2611
Nonlinear Least Squares: Newton-typeMethods......Page 2612
Nonlinear Least Squares Problems......Page 2619
Nonlinear Least Squares: Trust RegionMethods......Page 2623
Nonlinear Systems of Equations: Application to the Enclosure of All Azeotropes......Page 2630
Nonlocal Sensitivity Analysis with Automatic Differentiation......Page 2635
NonorientedMulticommodity Flow Problems......Page 2640
Nonsmooth Analysis: Fréchet Subdifferentials......Page 2644
Nonsmooth Analysis: Weak Stationarity......Page 2651
Nonsmooth Optimization Approach to Clustering......Page 2658
Nonsmooth and Smoothing Methods for Nonlinear Complementarity Problems and Variational Inequalities......Page 2664
NP-complete Problems and Proof Methodology......Page 2668
NumericalMethods for Unary Optimization......Page 2675
OligopolisticMarket Equilibrium......Page 2683
Operations Research......Page 2686
Operations Research and Financial Markets......Page 2688
Operations Research Models for Supply Chain Management and Design......Page 2696
Optimal Control of a Flexible Arm......Page 2707
Optimal Design of Composite Structures......Page 2710
Optimal Design in Nonlinear Optics......Page 2717
Optimality Criteria forMultiphase Chemical Equilibrium......Page 2723
Optimal Planning of Offshore Oilfield Infrastructure......Page 2730
Optimal Sensor Scheduling......Page 2738
Optimal Solvent Design Approaches......Page 2742
Optimal Triangulations......Page 2749
Optimization in Ad Hoc Networks......Page 2756
Optimization Based Framework for Radiation Therapy......Page 2766
Optimization-Based Visualization......Page 2777
Optimization in Boolean Classification Problems......Page 2783
Optimization in Classifying Text Documents......Page 2788
Optimization and Decision Support Systems......Page 2795
Optimization with Equilibrium Constraints: A Piecewise SQP Approach......Page 2799
Optimization in Leveled Graphs......Page 2805
Optimization inMedical Imaging......Page 2812
Optimization in Operation of Electric and Energy Power Systems......Page 2816
Optimization Problems in Unit-Disk Graphs......Page 2824
Optimization Software......Page 2836
Optimization Strategies for Dynamic Systems......Page 2839
Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data......Page 2850
Optimization in Water Resources......Page 2855
Optimizing Facility Location with Euclidean and Rectilinear Distances......Page 2861
Order Complementarity......Page 2865
Oriented Matroids......Page 2870
Orthogonal Triangularization......Page 2878
OutrankingMethods......Page 2879
Overdetermined Systems of Linear Equations......Page 2886
Packet Annealing......Page 2889
Parallel Computing: Complexity Classes......Page 2892
Parallel Computing: Models......Page 2895
Parallel Heuristic Search......Page 2900
Parametric Global Optimization: Sensitivity......Page 2904
Parametric Linear Programming: Cost Simplex Algorithm......Page 2909
Parametric Mixed Integer Nonlinear Optimization......Page 2912
Parametric Optimization: Embeddings, Path Following and Singularities......Page 2916
Peptide Identification viaMixed-Integer Optimization......Page 2922
Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization......Page 2930
Phase Problem in X-ray Crystallography: Shake and Bake Approach......Page 2945
Piecewise Linear Network Flow Problems......Page 2950
Pivoting Algorithms for Linear Programming Generating Two Paths......Page 2957
Planning in the Process Industry......Page 2962
Plant Layout Problems and Optimization......Page 2971
Pontryagin Maximum Principle......Page 2979
Portfolio Selection: MarkowitzMean-varianceModel......Page 2982
Portfolio Selection andMulticriteria Analysis......Page 2988
Potential ReductionMethods for Linear Programming......Page 3000
PowellMethod......Page 3004
Practical Augmented Lagrangian Methods......Page 3006
PredictiveMethod for Interhelical Contacts in Alpha-Helical Proteins......Page 3015
Preference Disaggregation......Page 3023
Preference Disaggregation Approach: Basic Features, Examples fromFinancial DecisionMaking......Page 3034
Preference Modeling......Page 3047
Preprocessing in Stochastic Programming......Page 3050
Price of Robustness for Linear Optimization Problems......Page 3053
Principal PivotingMethods for Linear Complementarity Problems......Page 3059
Probabilistic Analysis of Simplex Algorithms......Page 3065
Probabilistic Constrained Linear Programming: Duality Theory......Page 3076
Probabilistic Constrained Problems: Convexity Theory......Page 3079
Production-Distribution System Design Problem......Page 3080
Protein Folding: Generalized-Ensemble Algorithms......Page 3090
Protein Loop Structure PredictionMethods......Page 3092
Pseudomonotone Maps: Properties and Applications......Page 3097
QBB Global OptimizationMethod......Page 3103
QR Factorization......Page 3108
Quadratic Assignment Problem......Page 3111
Quadratic Fractional Programming: Dinkelbach Method......Page 3141
Quadratic Integer Programming: Complexity and Equivalent Forms......Page 3145
Quadratic Knapsack......Page 3151
Quadratic Programming with Bound Constraints......Page 3153
Quadratic Programming over an Ellipsoid......Page 3158
Quadratic Semi-assignment Problem......Page 3162
QuasidifferentiableOptimization......Page 3163
QuasidifferentiableOptimization: Algorithms for Hypodifferentiable Functions......Page 3168
QuasidifferentiableOptimization: Algorithms for QD Functions......Page 3170
QuasidifferentiableOptimization: Applications......Page 3176
Quasidifferentiable Optimization: Applications to Thermoelasticity......Page 3179
QuasidifferentiableOptimization: Calculus of Quasidifferentials......Page 3182
QuasidifferentiableOptimization: Codifferentiable Functions......Page 3186
Quasidifferentiable Optimization: Dini Derivatives, Clarke Derivatives......Page 3189
QuasidifferentiableOptimization: Exact Penalty Methods......Page 3192
Quasidifferentiable Optimization: Optimality Conditions......Page 3197
Quasidifferentiable Optimization: Stability of Dynamic Systems......Page 3205
QuasidifferentiableOptimization: Variational Formulations......Page 3209
Quasivariational Inequalities......Page 3213
Railroad Crew Scheduling......Page 3219
Railroad Locomotive Scheduling......Page 3228
Random Search Methods......Page 3237
Reactive Scheduling of Batch Processes......Page 3243
Redundancy in Nonlinear Programs......Page 3254
Reformulation-Linearization Technique for Global Optimization......Page 3255
Regression by Special Functions: Algorithms and Complexity......Page 3260
Relaxation in Projection Methods......Page 3265
Replicator Dynamics in Combinatorial Optimization......Page 3271
Resource Allocation for Epidemic Control......Page 3283
Reverse Convex Optimization......Page 3287
Robust Control......Page 3292
Robust Control: Schur Stability of Polytopes of Polynomials......Page 3297
Robust Design of Dynamic Systems by Constructive Nonlinear Dynamics......Page 3299
Robust Global Optimization......Page 3306
Robust Linear Programming with Right-Hand-Side Uncertainty, Duality and Applications......Page 3309
Robust Optimization......Page 3319
Robust Optimization: Mixed-Integer Linear Programs......Page 3323
Rosenbrock Method......Page 3335
Rosen’sMethod, Global Convergence, and Powell’s Conjecture......Page 3337
Saddle Point Theory and Optimality Conditions......Page 3347
Second Order Constraint Qualifications......Page 3349
Second Order Optimality Conditions for Nonlinear Optimization......Page 3353
Selection ofMaximally Informative Genes......Page 3357
Selfdual ParametricMethod for Linear Programs......Page 3366
Semidefinite Programming and Determinant Maximization......Page 3367
Semidefinite Programming: Optimality Conditions and Stability......Page 3372
Semidefinite Programming and the Sensor Network Localization Problem, SNLP......Page 3377
Semidefinite Programming and Structural Optimization......Page 3382
Semi-infinite Programming and Applications in Finance......Page 3388
Semi-infinite Programming: ApproximationMethods......Page 3397
Semi-infinite Programming and Control Problems......Page 3400
Semi-infinite Programming: DiscretizationMethods......Page 3409
Semi-infinite Programming: Methods for Linear Problems......Page 3416
Semi-infinite Programming: NumericalMethods......Page 3421
Semi-infinite Programming: Second Order Optimality Conditions......Page 3426
Semi-infinite Programming, Semidefinite Programming and Perfect Duality......Page 3431
Sensitivity Analysis of Complementarity Problems......Page 3437
Sensitivity Analysis of Variational Inequality Problems......Page 3439
Sensitivity and Stability in NLP......Page 3442
Sensitivity and Stability in NLP: Approximation......Page 3446
Sensitivity and Stability in NLP: Continuity and Differential Stability......Page 3459
Sequential Cutting Plane Algorithm......Page 3463
Sequential Quadratic Programming: Interior PointMethods for DistributedOptimal Control Problems......Page 3468
Sequential SimplexMethod......Page 3471
Set Covering, Packing and Partitioning Problems......Page 3474
Set-valued Optimization......Page 3478
Shape Optimization......Page 3480
Shape ReconstructionMethods for Nonconvex Feasibility Analysis......Page 3483
Shape Selective Zeolite Separation and Catalysis: OptimizationMethods......Page 3492
Shor, Naum Zuselevich......Page 3497
Shortest Path Tree Algorithms......Page 3499
Short-Term Scheduling of Batch Processes with Resources......Page 3511
Short-Term Scheduling of Continuous Processes......Page 3525
Short-Term Scheduling, Resource Constrained: UnifiedModeling Frameworks......Page 3539
Short-Term Scheduling Under Uncertainty: Sensitivity Analysis......Page 3552
Signal Processing with Higher Order Statistics......Page 3559
Simple Recourse Problem: Dual Method......Page 3563
Simple Recourse Problem: PrimalMethod......Page 3565
Simplicial Decomposition......Page 3567
Simplicial Decomposition Algorithms......Page 3571
Simplicial Pivoting Algorithms for Integer Programming......Page 3577
Simulated Annealing......Page 3583
Simulated AnnealingMethods in Protein Folding......Page 3585
Simultaneous Estimation and Optimization of Nonlinear Problems......Page 3590
Single Facility Location: Circle Covering Problem......Page 3599
Single Facility Location: Multi-objective Euclidean Distance Location......Page 3602
Single Facility Location: Multi-objective Rectilinear Distance Location......Page 3605
Smoothing Methods for Semi-Infinite Optimization......Page 3609
Smooth Nonlinear Nonconvex Optimization......Page 3614
Solution Methods for Multivalued Variational Inequalities......Page 3617
Solving Hemivariational Inequalities by Nonsmooth Optimization Methods......Page 3631
Solving Large Scale and Sparse Semidefinite Programs......Page 3635
Spatial Price Equilibrium......Page 3639
Spectral Projected GradientMethods......Page 3644
SplittingMethod for Linear Complementarity Problems......Page 3651
SSCMinimization Algorithms......Page 3654
SSCMinimization Algorithms for Nonsmooth and Stochastic Optimization......Page 3657
Stabilization of Cutting Plane Algorithms for Stochastic Linear Programming Problems......Page 3661
Stable Set Problem: Branch & Cut Algorithms......Page 3668
Standard Quadratic Optimization Problems: Algorithms......Page 3680
Standard Quadratic Optimization Problems: Applications......Page 3682
Standard Quadratic Optimization Problems: Theory......Page 3684
State of the Art inModeling Agricultural Systems......Page 3686
Static Resource Constrained Project Scheduling......Page 3696
Static Stochastic Programming Models......Page 3700
Static Stochastic Programming Models: Conditional Expectations......Page 3702
Statistical Classification: Optimization Approaches......Page 3703
Statistical Convergence and Turnpike Theory......Page 3705
Steiner Ratio of Biomolecular Structures......Page 3710
Steiner Tree Problems......Page 3715
Stochastic Bilevel Programs......Page 3728
Stochastic Global Optimization: Stopping Rules......Page 3735
Stochastic Global Optimization: Two-PhaseMethods......Page 3738
Stochastic Integer Programming: Continuity, Stability, Rates of Convergence......Page 3742
Stochastic Integer Programs......Page 3745
Stochastic Linear Programming: Decomposition and Cutting Planes......Page 3747
Stochastic Linear Programs with Recourse and Arbitrary Multivariate Distributions......Page 3752
Stochastic Network Problems: Massively Parallel Solution......Page 3757
Stochastic Optimal Stopping: NumericalMethods......Page 3765
Stochastic Optimal Stopping: ProblemFormulations......Page 3767
Stochastic Programming: Minimax Approach......Page 3770
Stochastic Programming Models: Random Objective......Page 3774
Stochastic Programming: Nonanticipativity and LagrangeMultipliers......Page 3775
Stochastic Programming: Parallel Factorization of StructuredMatrices......Page 3782
Stochastic Programming with Simple Integer Recourse......Page 3787
Stochastic Programs with Recourse: Upper Bounds......Page 3789
Stochastic QuasigradientMethods......Page 3794
Stochastic QuasigradientMethods: Applications......Page 3799
Stochastic QuasigradientMethods inMinimax Problems......Page 3805
Stochastic Scheduling......Page 3810
Stochastic Transportation and Location Problems......Page 3816
Stochastic Vehicle Routing Problems......Page 3821
Structural Optimization......Page 3824
Structural Optimization: History......Page 3826
Suboptimal Control......Page 3828
Successive Quadratic Programming......Page 3831
Successive Quadratic Programming: Applications in Distillation Systems......Page 3838
Successive Quadratic Programming: Applications in the Process Industry......Page 3845
Successive Quadratic Programming: DecompositionMethods......Page 3858
Successive Quadratic Programming: Full SpaceMethods......Page 3863
Successive Quadratic Programming: Solution by Active Sets and Interior Point Methods......Page 3870
Supply Chain Performance Measurement......Page 3876
Survivable Networks......Page 3881
Symmetric Systems of Linear Equations......Page 3884
Theorems of the Alternative and Optimization......Page 3887
Time-Dependent Traveling Salesman Problem......Page 3894
Topological Derivative in Shape Optimization......Page 3900
TopologicalMethods in Complementarity Theory......Page 3910
Topology of Global Optimization......Page 3914
Topology Optimization......Page 3920
Traffic Network Equilibrium......Page 3921
Traveling Salesman Problem......Page 3927
Tucker Homogeneous Systems of Linear Relations......Page 3936
Turnpike Theory: Stability of Optimal Trajectories......Page 3940
Two-Stage Stochastic Programming: QuasigradientMethod......Page 3947
Two-Stage Stochastic Programs with Recourse......Page 3951
Unconstrained Nonlinear Optimization: Newton–Cauchy Framework......Page 3954
Unconstrained Optimization in Neural Network Training......Page 3959
Variable Neighborhood Search Methods......Page 3966
Variational Inequalities......Page 3980
Variational Inequalities: F. E. Approach......Page 3985
Variational Inequalities: Geometric Interpretation, Existence and Uniqueness......Page 3990
Variational Inequalities: Projected Dynamical System......Page 3993
Variational Principles......Page 3998
Vector Optimization......Page 4002
Vector Variational Inequalities......Page 4005
Vehicle Routing......Page 4010
Vehicle Routing Problem with Simultaneous Pickups and Deliveries......Page 4013
Vehicle Scheduling......Page 4018
Volume Computation for Polytopes: Strategies and Performances......Page 4023
Von Neumann, John......Page 4029
Voronoi Diagrams in Facility Location......Page 4031
Walrasian Price Equilibrium......Page 4037
Warehouse Location Problem......Page 4040
Wastewater System, Optimization of......Page 4045
Young Programming......Page 4051