Numerical methods for constrained optimization

✍ Scribed by Gill P., Murray W.

• Publisher: AP
• Year: 1975
• Tongue: English
• Leaves: 298
• Category: Library

✦ Synopsis

Logistics is defined as a business planning framework for the management of material, service, information and capital flows. Logistic systems have received considerable attention in the last 10 years, as they constitute one of the cornerstones in the design and control of production systems and the modeling of supply chains. This renewed interest is partly due to the recognition that well-known planning and control systems such as ‘Manufacturing Resources Planning’ and ‘Just in Time’ systems fail to establish a sound integration of lead time management, capacity planning and quality considerations.This book uniquely:Presents a balanced treatment of quantitative methods for logistics systems planning, organization and control.Each topic is illustrated with real examples.Each chapter features an annotated bibliography of key references.Features a number of case studies that show how the methods can be applied to complex logistics problems.Assumes only a basic knowledge of operations research.Supported by a Website (http://wileylogisticsbook.dii.unile.it) featuring exercises and teaching material.A unique, leading edge title for researchers, practitioners, and students of logistics and supply chain management, in both academia; engineering, computer science, management science, undergraduate, graduate students and industry professionals

✦ Table of Contents

title......Page img001_2R.djvu
copyright......Page img002_1L.djvu
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