Numerical Methods for Constrained Optimization

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Contributors......Page img002_2R.djvu
Preface......Page img003_2R.djvu
A Glossary of Symbols ......Page img004_2R.djvu
Contents ......Page img005_2R.djvu
1.1. Descent Methods for Minimization ......Page img008_2R.djvu
1.2. First-order Conditions for a Solution ......Page img010_1L.djvu
1.3. Second-order Conditions for a Solution ......Page img012_1L.djvu
1.4. Some Active Set Strategies and Quadratic Programming ......Page img015_1L.djvu
1.5. Lagrangian Functions ......Page img018_2R.djvu
2.1. Introduction ......Page img022_2R.djvu
2.2. Geometrical Considerations and Conditions for a Solution ......Page img023_1L.djvu
2.3. Newton-type Methods for Unconstrained Minimization ......Page img024_1L.djvu
2.4. Minimization with Linear Equality Constraints—a Survey ......Page img028_1L.djvu
2.5. A Projected Newton-type Method for the Equality-constraint Problem ......Page img030_2R.djvu
2.6. Determination of the Set of Active Constraints ......Page img033_1L.djvu
2.7. Degeneracy ......Page img036_1L.djvu
2.8. Computing and Updating the Matrix Z ......Page img036_2R.djvu
2.9. Finding an Initial Feasible Point ......Page img039_2R.djvu
2.10. Conclusions ......Page img040_2R.djvu
3.1. Introduction ......Page img041_2R.djvu
3.2. Linearly Constrained Optimization—Historical Developments ......Page img042_2R.djvu
3.3. Revised Quasi-Newton Methods ......Page img045_1L.djvu
3.4. Factorized Forms of the Standard Algorithms ......Page img046_2R.djvu
3.5. The Choice of Active Set ......Page img048_1L.djvu
3.6. Linearly Constrained Algorithms which do not Require Derivatives ......Page img052_2R.djvu
3.7. Methods Based upon Solving a Quadratic and Linear Program at Each Iteration  ......Page img053_1L.djvu
4.1. Introduction ......Page img054_2R.djvu
4.3. Direct Methods based upon Matrix Factorizations ......Page img056_1L.djvu
4.4. Pre-processing Techniques ......Page img062_2R.djvu
4.5. Updating the Factorizations ......Page img064_2R.djvu
4.6. Conjugate-gradient Methods ......Page img069_1L.djvu
4.7. Iterative Methods for the Solution of Large Sparse Sets of Linear Equations ......Page img070_1L.djvu
4.8. Newton-type Methods with Second Derivatives Available ......Page img071_1L.djvu
4.9. Methods Using Only First Derivatives ......Page img072_2R.djvu
4.10. Methods Using No Derivatives ......Page img073_2R.djvu
4.11. General Problems ......Page img074_1L.djvu
4.12. Large-scale Linear Programming ......Page img075_2R.djvu
4.13. Simple Constraints ......Page img076_2R.djvu
4.16. Structured Problems ......Page img077_2R.djvu
4.17. Decomposition Techniques ......Page img079_1L.djvu
4.18. Concluding Remarks ......Page img081_2R.djvu
5.1. Introduction ......Page img082_2R.djvu
5.2. Minimization Subject to Equality Constraints ......Page img083_1L.djvu
5.3. Inequality Constraints—Active Set Strategies ......Page img090_2R.djvu
5.4. Summary ......Page img094_2R.djvu
6.1. Introduction ......Page img095_2R.djvu
6.2. Transformation Methods ......Page img096_2R.djvu
6.3. Barrier Functions ......Page img097_1L.djvu
6.4. Barrier-Function Strengths ......Page img097_2R.djvu
6.5. Barrier-Function Weaknesses ......Page img099_1L.djvu
6.6. Penalty Functions ......Page img100_2R.djvu
6.7. Recent Contributions ......Page img101_1L.djvu
7.1. Introduction ......Page img103_2R.djvu
7.2. Monte Carlo Methods ......Page img104_2R.djvu
7.3. Rejection of Non-feasible Points ......Page img105_1L.djvu
7.4. Self-bounding Methods ......Page img105_2R.djvu
7.5. The Probe Method ......Page img106_1L.djvu
7.6. Constraint Following in Pattern Search ......Page img106_2R.djvu
7.7. DSC with Linear Constraints ......Page img107_2R.djvu
7.8. Transformation Methods : Penalty Functions ......Page img108_2R.djvu
7.9. Simpat ......Page img109_1L.djvu
7.10. Transformation Methods: Barrier Functions ......Page img109_2R.djvu
7.11. The Complex Method of Box ......Page img112_1L.djvu
7.12. Variations of the Complex Method ......Page img113_1L.djvu
7.13. ACSIM ......Page img114_2R.djvu
7.14. Conclusion ......Page img116_2R.djvu
8.1. Introduction ......Page img117_2R.djvu
8.2. The Powell-Hestenes Penalty Function ......Page img118_2R.djvu
8.3. The Rockafellar Generalization ......Page img120_2R.djvu
8.4. Murray's Method ......Page img122_1L.djvu
8.5. Methods with Second-order Convergence ......Page img123_1L.djvu
8.6. Fletcher's Method ......Page img125_2R.djvu
9.1. Introduction ......Page img128_2R.djvu
9.2. Sources of Computer Listings ......Page img129_1L.djvu
9.3. Test Problems and Comparative Evaluation of Algorithms ......Page img129_2R.djvu
9.4. Unconstrained Optimization ......Page img131_1L.djvu
9.5. Linearly Constrained Optimization ......Page img131_2R.djvu
9.6. Nonlinearly Constrained Optimization ......Page img132_1L.djvu
9.7. Global Optimization ......Page img133_1L.djvu
9.8. Convergence Proofs and Rates of Convergence ......Page img135_1L.djvu
9.9. Scaling ......Page img136_2R.djvu
References ......Page img138_2R.djvu
Author Index ......Page img142_2R.djvu
Subject Index ......Page img144_2R.djvu