Chinchuluun / Pardalos / Enkhbat Optimization and Optimal Control

Theory and Applications
1. Auflage 2010
ISBN: 978-0-387-89496-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 39, 510 Seiten

Reihe: Springer Optimization and Its Applications

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. 'Optimization and Optimal Control: Theory and Applications' brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems.This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.

Prof. Pardalos is a distinguished Springer author and recognized throughout the world as a first rate mathematician. Prof. Rentsen has an extensive CV and list of publications, and he has organized the first and second International Conference for Optimization and Optimal Control (2002, 2007) in Mongolia.  (We might be able to possibly do a bulk sale for his book for the 3rd international conference.)  Pardalos, Tseveendorj, Enkhbat have edited a volume together before with World Scientific. 'Optimization and Optimal Control' (World Scientific, 978-9812385970, $106, 2003) Prof. Chinchuluun has recently helped Pardalos with another optimization edited volume which will be available in 2008.

Autoren/Hrsg.

Chinchuluun, Altannar

Enkhbat, Rentsen

Tseveendorj, Ider

Pardalos, Panos M.

Inhaltsverzeichnis

1;Preface;7
2;Contents;10
3;Sensibility Function as Convolution of System of Optimization Problems ;13
3.1;1 Introduction;13
3.2;2 Optimization Problems for the Sensibility Function;19
3.3;3 Primal Extraproximal Method;23
3.3.1;3.1 Primal method;24
3.4;4 Dual Extraproximal Method;29
3.4.1;4.1 Dual Method;29
3.5;5 Conclusions;32
3.6;References;32
4;Post-optimal Analysis of Linear Semi-infinite Programs;34
4.1;1 Introduction;34
4.2;2 Preliminaries;42
4.2.1;2.1 Basic Concepts on Sets and Mappings;42
4.2.2;2.2 Basic Concepts and Results on LSIP;43
4.2.3;2.3 Perturbed LSIP Problems;45
4.3;3 Perturbing All the Data;47
4.3.1;3.1 Stability of the Feasible Set;47
4.3.2;3.2 Stability of the Optimal Set;49
4.3.3;3.3 Stability of the Optimal Value and Well-Posedness;49
4.3.4;3.4 Distance to Ill-Posedness;50
4.3.5;3.5 Error Bounds;50
4.3.6;3.6 Primal--Dual Stability;51
4.4;4 Perturbing the Cost Vector and the RHS Function;52
4.4.1;4.1 Stability Analysis;52
4.4.2;4.2 Sensitivity Analysis;53
4.5;5 Perturbing the RHS Function;54
4.5.1;5.1 Stability Analysis;54
4.5.2;5.2 Sensitivity Analysis;54
4.6;6 Perturbing the Cost Vector;55
4.6.1;6.1 Stability Analysis;55
4.6.2;6.2 Sensitivity Analysis;56
4.7;7 Conclusions;57
4.8;References;58
5;On Equilibrium Problems;65
5.1;1 Introduction;65
5.2;2 The Equilibrium Problem and Its Important Particular Cases;66
5.2.1;2.1 The Minimum Problem;67
5.2.2;2.2 The Kirszbraun's Problem;67
5.2.3;2.3 The Saddlepoint (Minimax Theorems);68
5.2.3.1;2.3.1 Two-Player Zero-Sum Games;69
5.2.3.2;2.3.2 Duality in Optimization;70
5.2.4;2.4 Variational Inequalities;72
5.3;3 Some Existence Results on Equilibrium Problem;74
5.3.1;3.1 Results Based on Fixed Point Theorems;74
5.3.2;3.2 Results Based on Separation Theorems;79
5.4;4 The Equilibrium Problem and the Ekeland's Principle;81
5.4.1;4.1 The Ekeland's Principle for (EP) and (SEP);82
5.4.2;4.2 New Existence Results for Equilibria on Compact Sets;87
5.4.3;4.3 Equilibria on Noncompact Sets;88
5.5;5 Conclusions;90
5.6;References;91
6;Scalarly Compactness, (S)+-Type Conditions, Variational Inequalities, and Complementarity Problems in Banach Spaces ;94
6.1;1 Introduction;94
6.2;2 Preliminaries;95
6.3;3 (S)+-Type Conditions;96
6.4;4 Scalar Asymptotic Derivatives;99
6.5;5 Scalar Compactness;100
6.6;6 Existence Theorems for Variational Inequalities and Complementarity Problems;106
6.7;7 Comments;112
6.8;References;112
7;Quasi-equilibrium Inclusion Problemsof the Blum--Oettli-Type and Related Problems;114
7.1;1 Introduction;114
7.2;2 Preliminaries and definitions;116
7.3;3 Main Results;118
7.4;References;128
8;General Quadratic Programming and Its Applications in Response Surface Analysis;129
8.1;1 Introduction;129
8.2;2 Response Surface Methodology;131
8.3;3 Quadratic Convex Maximization Problem;133
8.4;4 Indefinite Quadratic Programming;135
8.5;5 Quadratic Convex Minimization Problem;138
8.5.1;5.1 Response Surface Practical Problems;139
8.6;6 Conclusion;144
8.7;References;144
9;Canonical Dual Solutions for Fixed Cost Quadratic Programs;146
9.1;1 Primal Problem and Motivation;146
9.2;2 Canonical Dual Problem;147
9.3;3 Global Optimality Criteria;152
9.4;4 Existence and Uniqueness Criteria;155
9.5;5 Application to Decoupled Problem ;157
9.6;6 Examples;158
9.6.1;6.1 Two-Dimensional Decoupled Problem;158
9.6.2;6.2 General Nonconvex Problem;159
9.7;7 Concluding Remarks and Open Problems;159
9.8;References;161
10;Algorithms of Quasidifferentiable Optimization for the Separation of Point Sets;164
10.1;1 Introduction;164
10.2;2 Basic Notions;165
10.3;3 Quasidifferential Calculus;165
10.3.1;3.1 Necessary Optimality Conditions;167
10.4;4 Principal Algorithm of Finding the Intersection of Two Sets;167
10.5;5 A Minimization Method Due to Bagirov;169
10.6;6 Algorithm INTERSEC;172
10.7;7 Preliminary Numerical Results;173
10.8;References;173
11;A Hybrid Evolutionary Algorithmfor Global Optimization ;175
11.1;1 Introduction;175
11.2;2 Evolutionary Algorithm;177
11.2.1;2.1 Basic Schemes;177
11.2.2;2.2 Procedures Used in Evolutionary Algorithm;178
11.3;3 Hybrid Evolutionary Algorithm;178
11.3.1;3.1 Modification of the Fitness Function;179
11.3.2;3.2 Population Update Rules;183
11.3.3;3.3 HEA Algorithm;185
11.4;4 Numerical Experiments;186
11.5;5 Conclusions;189
11.6;References;189
12;Gap Functions for Vector Equilibrium Problems via Conjugate Duality;191
12.1;1 Introduction;191
12.2;2 Mathematical Preliminaries;192
12.3;3 The Constrained Vector Optimization Problem;195
12.3.1;3.1 Different Dual Problems;195
12.3.2;3.2 Stability and Strong Duality;197
12.4;4 Gap Functions for Vector Equilibrium Problems;200
12.5;5 Conclusions;202
12.6;References;203
13;Polynomially Solvable Cases of Binary Quadratic Programs;204
13.1;1 Introduction;205
13.2;2 Problem (0--1QP) with All Off-Diagonal Elements of Q Being Non-positive;207
13.3;3 Problem (0--1QPh) with Fixed Rank Q;210
13.4;4 Problem (0--1QP) with Q Being a Tridiagonal Matrix;214
13.5;5 Problem (BQP) Defined by a Series-Parallel Graph;217
13.6;6 Problem (0--1QP) Defined by a Logic Circuit;223
13.7;7 SDP Representation of Lagrangian Dual and Polynomial Solvability;226
13.8;8 Conclusions;228
13.9;References;229
14;Generalized Solutions of Multi-valued Monotone Quasi-variational Inequalities;231
14.1;1 Introduction;231
14.2;2 Main Results;234
14.3;3 Applications;241
14.3.1;3.1 Quasi-hemivariational Inequalities;241
14.3.2;3.2 Inverse Problems;241
14.4;4 Concluding Remarks;242
14.5;References;242
15;Optimal Feedback Control for Stochastic Impulsive Linear Systems Subject to Poisson Processes ;245
15.1;1 Introduction;245
15.2;2 Problem Statement;247
15.3;3 Deterministic Transformation;249
15.4;4 Time Scaling Transformation;253
15.5;5 Gradient Formulae;254
15.6;6 Example;256
15.7;7 Conclusion;261
15.8;References;261
16;Analysis of Differential Inclusions: Feedback Control Method;263
16.1;1 Introduction;263
16.2;2 Statement of the Problems;267
16.3;3 The Algorithm for Solving Problem 1;270
16.4;4 The Algorithm for Solving Problem 2;270
16.5;5 The Algorithm for Solving Problem 3;275
16.6;6 Conclusion;279
16.7;References;279
17;A Game Theoretic Algorithm to Solve Riccati and Hamilton--Jacobi--Bellman--Isaacs (HJBI) Equations in H Control ;280
17.1;1 Introduction;280
17.2;2 Solving the LQ Problem by the Kleinman Algorithm;285
17.3;3 Solving H Riccati Equations;286
17.3.1;3.1 The Summarizing Theorem;287
17.3.2;3.2 Algorithm;288
17.3.3;3.3 Rate of Convergence;289
17.3.4;3.4 Game Theoretic Interpretation of the Algorithm;291
17.3.5;3.5 Numerical Examples;293
17.4;4 Solving an HJB Equation by a Sequenceof Linear PDEs;297
17.4.1;4.1 t1 Is Finite;298
17.4.2;4.2 t1 Is Infinite;299
17.5;5 Solving an HJBI Equation by a Sequenceof HJB Equations;301
17.5.1;5.1 Preliminaries and Definitions;301
17.5.2;5.2 The Summarizing Theorem;303
17.5.3;5.3 Algorithm;305
17.5.4;5.4 Rate of Convergence and Game Theoretic Interpretation;306
17.5.5;5.5 A Numerical Example;306
17.6;6 Conclusions;308
17.7;References;309
18;Online Adaptive Optimal Control Based on Reinforcement Learning ;312
18.1;1 Introduction;312
18.2;2 The Continuous-Time Optimal Control Problem;316
18.3;3 The Policy Iteration Algorithm;317
18.4;4 Online Adaptive Optimal Control Solution Using Neural Network Elements in an Actor--Critic Structure;319
18.5;5 Simulation Results;322
18.6;6 Conclusions;324
18.7;References;325
19;Perturbation Methods in Optimal Control Problems;327
19.1;1 Introduction;327
19.2;2 The Perturbation Methods in Optimal Control Problems That Are Polynomial with Respect to State;329
19.2.1;2.1 The Optimal Control Problem That Is Polynomialwith Respect to State;329
19.2.2;2.2 Perturbation Method for Boundary-Value Improvement Problem;332
19.2.3;2.3 Transformation Method for Perturbed Boundary-Value Improvement Problems ;339
19.2.4;2.4 Perturbation Method for Improvement Condition in Control Space;344
19.2.5;2.5 Projective Perturbation Method for Improvement Condition;355
19.3;3 Perturbation Methods in the Main Optimal Control Problem;357
19.3.1;3.1 The Main Optimal Control Problem ;358
19.3.2;3.2 Perturbation Method for Maximum Principle;360
19.3.3;3.3 Projective Perturbation Method for Optimality Condition ;367
19.3.4;3.4 Numerical Solution for Test Case ;371
19.4;4 Conclusion;374
19.5;References;375
20;Stochastic Optimal Control with Applications in Financial Engineering;376
20.1;1 Introduction;376
20.2;2 Deterministic Optimal Control;379
20.2.1;2.1 Theory;379
20.2.2;2.2 Example: An LQ Optimal Control Problem;381
20.3;3 Stochastic Optimal Control;383
20.3.1;3.1 Stochastic Processes;383
20.3.2;3.2 Stochastic Differential Equations;384
20.3.3;3.3 Stochastic Calculus;385
20.3.4;3.4 Stochastic Optimal Control Theory;386
20.3.5;3.5 Example: An LQ Optimal Control Problem;387
20.4;4 Applications in Financial Engineering;389
20.4.1;4.1 Introduction;389
20.4.2;4.2 Utility Functions;390
20.4.3;4.3 Wealth Dynamics;391
20.4.3.1;4.3.1 Risk-Free Money Market Account;391
20.4.3.2;4.3.2 Risky Investments;391
20.4.3.3;4.3.3 Economic Influence Factors;391
20.4.3.4;4.3.4 Wealth Dynamics;392
20.4.4;4.4 CRRA Problems;393
20.4.5;4.5 CARA Problems;399
20.5;5 Conclusions;403
20.6;References;404
21;A Nonlinear Optimal Control Approach to Process Scheduling;410
21.1;1 Introduction;410
21.2;2 Crude Oil Scheduling Models;412
21.2.1;2.1 Modeling the Transfer Operation;413
21.2.2;2.2 Optimal Control Nonlinear Model;415
21.2.3;2.3 Solving the Problem;418
21.2.4;2.4 Mixed-Integer Linear Model;418
21.3;3 Results;419
21.4;4 Conclusion;421
21.5;References;421
22;Hadamard's Matrices, Grothendieck's Constant,and Root Two;423
22.1;1 Introduction;423
22.2;2 Quantum Background;424
22.2.1;2.1 Computational State Space;424
22.2.2;2.2 Entanglement;424
22.2.3;2.3 Observable State Space;426
22.2.4;2.4 SU(v) Representation;427
22.2.5;2.5 Amplitude Amplification;428
22.2.6;2.6 Correlation Matrices;429
22.3;3 The Multiknapsack Multiplayer Game Model;430
22.4;4 The Multiknapsack Quantum Simulation;432
22.5;5 The Multiknapsack Entanglement Issues;434
22.6;6 Hadamard Matrices and Fishburn and Reeds Formulation;435
22.7;7 Lehman Matrices and Grothendieck's Constant;438
22.8;8 Grothendieck's Constant and Root 2 Issues;440
22.8.1;8.1 2-(v,k,0=x"0115)2 Designs;440
22.8.2;8.2 Classical/Quantum Metaheuristics Issues;441
22.8.3;8.3 Quantum Oddities;442
22.9;9 Concluding Remarks;444
22.10;References;445
23;On the Pasture Territories Covering Maximal Grass ;448
23.1;1 Main Concepts and the Problem Definition;448
23.2;2 On the Forms of Exploiting Pasture Territories in Simple Cases;451
23.3;3 Some Solution Properties of the Main Maximization Problem on the Plane;455
23.4;4 Conclusion;459
23.5;References;460
24;On Solvability of the Rate Control Problemin Wired-cum-Wireless Networks;461
24.1;1 Introduction;461
24.2;2 Related Works;463
24.3;3 The Rate Control Problem;464
24.4;4 Solvability of the Rate Control Problem;466
24.5;5 Numerical Example;469
24.6;6 Conclusion;471
24.7;References;476
25;Integer Programming of Biclustering Basedon Graph Models ;477
25.1;1 Introduction;477
25.2;2 Biclustering Models;478
25.3;3 General Approach to Biclustering;479
25.3.1;3.1 Graph Partitioning;479
25.3.2;3.2 Bipartite Partitioning and Biclustering;481
25.4;4 Integer Programming of Partitioning;482
25.4.1;4.1 Ratio Cut;487
25.4.2;4.2 Normalized Cut and Minmax Cut;490
25.4.3;4.3 ICA Cut;493
25.4.4;4.4 Spectral and Integer Programming Biclustering;495
25.5;5 Conclusion;495
25.6;References;495
26;A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals ;497
26.1;1 Introduction;497
26.2;2 Proof of Theorem 1;500
26.3;3 Concluding Remark;507
26.4;References;507