Cover Image

Stable parametric programming /

Show other versions (1)

Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex prog...

Full description

Bibliographic Details
Main Author: Zlobec, S.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht, the Netherlands ; Boston, MA : Kluwer Academic Publishers, [2001]
Series:Applied optimization ; v. 57.
Subjects:
Programming (Mathematics)
Mathematical optimization.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1 Parametric Programming in Ancient Times 1
  • 2 Motivation 3
  • 3 Stable Linear Models 4
  • 4 Unstable Linear Models 7
  • 5 Idea of Input Optimization 8
  • 2 Classical Optimality Conditions 11
  • 1 Method of Lagrange 12
  • 2 Second-Order Optimality Conditions 14
  • 3 Basic Convex Programming 29
  • 1 Convex Sets 29
  • 2 Convex Functions 32
  • 3 Systems of Convex Inequalities 36
  • 4 Optimality Conditions 38
  • 4 Asymptotic Optimality Conditions 59
  • 1 Convex LFS Functions 59
  • 2 Convex Programs with LFS Constraints 61
  • 3 General Convex Programs 62
  • 5 Non-Smooth Programs 73
  • 2 Optimality for Non-Smooth Programs 73
  • 3 Non-Smooth LFS Functions 75
  • 4 An Equivalent Unconstrained Program 79
  • 6 Multi-Objective Programs 87
  • 2 Pareto Optima for LFS Functions 88
  • 3 Pareto Optima for Differentiable Functions 90
  • 4 Saddle-Point Characterization 92
  • 7 Introduction to Stability 101
  • 2 Point-to-Set Mappings 102
  • 3 Stable Convex Models 104
  • 4 Regions of Stability 108
  • 8 Locally Optimal Parameters 121
  • 1 Characterizing Locally Optimal Parameters 121
  • 2 Input Constraint Qualifications 124
  • 3 Lagrange Point-to-Set Mappings 126
  • 9 Globally Optimal Parameters 135
  • 1 Characterizing Globally Optimal Parameters 135
  • 2 Sandwich Condition 137
  • 3 Optimality in LFS Models 139
  • 4 Duality 140
  • 5 An Explicit Representation of Optimal Parameters 145
  • 10 Optimal Value Function 155
  • 1 Marginal Value Formula 155
  • 2 Input Optimization 162
  • 3 Review of Minimum Principles 164
  • 4 Case Study: Restructuring in a Textile Mill 166
  • 5 Case Study: Planning of University Admission 170
  • 11 Partly Convex Programming 185
  • 1 Sources of Partly Convex Programs 186
  • 2 Characterizations of Global and Local Optima 191
  • 3 Partly LFS Programs 195
  • 12 Numerical Methods in PCP 203
  • 1 Parametric Steepest Descent Method 203
  • 2 Parametric Quasi-Newton Methods 205
  • 3 Constrained Programs 207
  • 13 Zermelo's Navigation Problems 213
  • 1 Zermelo's Problem on the Water 213
  • 2 Solution by the Method of Lagrange 215
  • 3 Solution by Input Optimization 216
  • 4 Zermelo's Problem under the Water 217
  • 5 Dual Solutions: Interpretation 219
  • 14 Efficiency Testing in Data Envelopment Analysis 225
  • 1 Charnes-Cooper-Rhodes Tests 225
  • 2 Stability of Charnes-Cooper-Rhodes Tests 230
  • 3 Stable Post-Optimality Analysis 231
  • 4 Radius of Rigidity Method 232
  • 5 Case Study: Efficiency Evaluations of University Libraries 236
  • 1 Linear Parametric Models 243
  • 2 Lexicographic Models 248
  • 3 Stable Inverse Programming 255
  • 4 Semi-Abstract Parametric Programming 257
  • 5 Abstract Parametric Programming 258
  • Appendix Method of Weierstrass 279.