This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia," the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications.
; March 2006
604 pages; ISBN 9780387242552Read online
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Title: Optimization and Control with Applications
Author: Liqun Qi; Kok Lay Teo; Xiao Qi Yang
Preface – Biographical Sketch of Elijah Polak – Publications of Elijah Polak – PART I. DUALITY AND OPTIMALITY CONDITIONS – Chapter 1. On Minimization of Max-Min Functions – Chapter 2. A Comparison of Two Approaches to Second-Order Subdifferentiability Concepts with Application to Optimality Conditions – Chapter 3. Duality and Exact Penalization via a Generalized Augmented Lagrangian Function – Chapter 4. Duality for Semi-Definite and Semi-Infinite Programming with Equality Constraints – Chapter 5. The Use of Nonsmooth Analysis and of Duality Methods for the Study of Hamilton-Jacobi Equations – Chapter 6. Some Classes of Abstract Convex Functions – PART II. OPTIMIZATION ALGORITHMS – Chapter 7. An Implementation of Training Dual-nu Support Vector Machines – Chapter 8. An Analysis of the Barzilai and Borwein Gradient Method for Unsymmetric Linear Equations – Chapter 9. An Exchange Algorithm for Minimizing Sum-Min Functions – Chapter 10. On the Barzlai-Borwein Method – Chapter 11. The Modified Subgradient Method for Equality Constrained Nonconvex Optimization Problems – Chapter 12. Inexact Restoration Methods for Nonlinear Programming: Advances and Perspectives – Chapter 13. Quantum Algorithm for Continuous Global Optimization – Chapter 14. SQP Versus SCP Methods for Nonlinear Programming – Chapter 15. An Approximation Approach for Linear Programming in Measure Space – PART III. OPTIMAL CONTROL – Chapter 16. Optimal Control of Nonlinear Systems – Chapter 17. Proximal-Like Methods for Convex Minimization Problems – Chapter 18. Analysis of Two Dimensional Nonconvex Variational Problems – Chapter 19. Stability of Equilibrium Points of Projected Dynamical Systems – Chapter 20. On a Quasi-Consistent Approximations Approach to Optimization Problems with Two Numerical Precision Parameters – Chapter 21. Numerical Solutions of Optimal Switching Control Problems – Chapter 22. A Solution to Hamilton-Jacobi Equation by NeuralNetworks and Optimal State Feedback Control – Chapter 23. H(infinity) Control Based on State Observer for Descriptor Systems – PART IV. VARIATIONAL INEQUALITY AND EQUILIBRIUM – Chapter 24. Decomposable Generalized Vector Variational Inequalities – Chapter 25. On a Geometric Lemma and Set-Valued Vector Equilibrium Problem – Chapter 26. Equilibrium Problems – Chapter 27. Gap Functions and Descent Methods for Minty Variational Inequality – Chapter 28. A New Class of Proximal Algorithms for the Nonlinear Complementary Problem