An Optimization Primer (Springer Series in Operations Research and Financial Engineering)

Preface
	How to Read the Book
	Supporting Material
Acknowledgements
Contents
1 PRELUDE
	1.A The Mathematical Curtain Rise
	1.B Data Smoothing
	1.C Optimization under Uncertainty
	1.D Convex Analysis
	1.E Estimation and Classification
	1.F Gradient Descent Method
	1.G Newton's Method
	1.H Acceleration and Regularization
	1.I Quasi-Newton Methods
	1.J Coordinate Descent Algorithms
2 CONVEX OPTIMIZATION
	2.A Formulations
	2.B Subderivatives and Subgradients
	2.C Subgradient Calculus
	2.D Proximal Gradient Methods
	2.E Linear Constraints
	2.F Karush-Kuhn-Tucker Condition
	2.G Interior-Point Method
	2.H Support Vector Machines
	2.I Subgradient Method
	2.J Conic Constraints
	2.K Polyhedral Analysis
3 OPTIMIZATION UNDER UNCERTAINTY
	3.A Product Mix Optimization
	3.B Expectation Functions
	3.C Risk Modeling
	3.D Models of Uncertainty
	3.E Risk-Adaptive Design
	3.F Optimality in Stochastic Optimization
	3.G Stochastic Gradient Descent
	3.H Simple Recourse Problems
	3.I Control of Water Pollution
	3.J Linear Recourse Problems
	3.K Network Capacity Expansion
4 MINIMIZATION PROBLEMS
	4.A Formulations
	4.B Network Design and Operation
	4.C Epigraphical Approximation Algorithm
	4.D Constraint Softening
	4.E Set Analysis
	4.F Robotic Path Planning
	4.G Tangent and Normal Cones I
	4.H Tangent and Normal Cones II
	4.I Subdifferentiability
	4.J Optimality Conditions
	4.K SQP and Interior-Point Methods
5 PERTURBATION AND DUALITY
	5.A Rockafellians
	5.B Quantitative Stability
	5.C Lagrangians and Dual Problems
	5.D Lagrangian Relaxation
	5.E Saddle Points
	5.F Strong Duality
	5.G Reformulations
	5.H L-Shaped Method
	5.I Monitoring Functions
	5.J Lagrangian Finite-Generation Method
6 WITHOUT CONVEXITY OR SMOOTHNESS
	6.A Second-Order Analysis
	6.B Augmented Lagrangians
	6.C Epigraphical Nesting
	6.D Optimality Conditions
	6.E Sup-Projections
	6.F Proximal Composite Method
	6.G Design of Multi-Component Systems
	6.H Difference-of-Convex Functions
	6.I DC in Regression and Classification
	6.J Approximation Errors
7 GENERALIZED EQUATIONS
	7.A Formulations
	7.B Equilibrium in Energy Markets
	7.C Traffic Equilibrium
	7.D Reformulation as Minimization Problems
	7.E Projection Methods
	7.F Nonsmooth Newton-Raphson Algorithm
	7.G Continuity of Set-Valued Mappings
	7.H Graphical Approximation Algorithm
	7.I Consistent Approximations
	7.J Approximation Errors
8 RISK MODELING AND SAMPLE  AVERAGES
	8.A Estimation of Optimality Gaps
	8.B Risk and Regret
	8.C Risk-Adaptive Data Analytics
	8.D Duality
	8.E Subgradients of Functionals
	8.F Residual Risk and Surrogates
	8.G Sample Average Approximations
	8.H Concentration Inequalities
	8.I Diametrical Stochastic Optimization
9 GAMES AND MINSUP PROBLEMS
	9.A Nash Games
	9.B Formulation as Minsup Problems
	9.C Bifunctions and Solutions
	9.D Lopsided Approximation Algorithm
	9.E Lop-Convergence I
	9.F Lop-Convergence II
	9.G Approximation of Games
	9.H Walras Barter Model
10 DECOMPOSITION
	10.A Proximal Alternating Gradient Method
	10.B Linkage Constraints
	10.C Progressive Decoupling Algorithm
	10.D Local Elicitation
	10.E Decoupling in Stochastic Optimization
	10.F Strong Monotonicity
	10.G Variational Convexity and Elicitation
	10.H Nonlinear Linkage
References
Index