Quadratic Programming and Affine Variational Inequalities - Gue Myung Lee

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Résumé :
This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. One special feature of the book is that when a certain property of a characteristic map or function is investigated, the authors always try first to establish necessary conditions for it to hold, then they go on to study whether the obtained necessary conditions are also sufficient ones. This helps to clarify the structures of the two classes of problems under consideration. The qualitative results can be used for dealing with algorithms and applications related to quadratic programming problems and affine variational inequalities.

Sommaire:
Preface?Notations and Abbreviations?1. Quadratic Programming Problems?2. Existence Theorems for Quadratic Programs?3. Necessary and Sufficient Optimality Conditions for Quadratic Programs?4. Properties of the Solution Sets of Quadratic Programs?5. Affine Variational Inequalities?6. Solution Existence for Affine Variational Inequalities?7. Upper-Lipschitz Continuity of the Solution Map in Affine Variational Inequalities?8. Linear Fractional Vector Optimization Problems?9. The Traffic Equilibrium Problem?10. Upper Semicontinuity of the KKT Point Set Mapping?11. Lower Semicontinuity of the KKT Point Set Mapping?12. Continuity of the Solution Map in Quadratic Programming?13. Continuity of the Optimal Value Function in Quadratic Programming?14. Directional Differentiability of the Optimal Value Function?15. Quadratic Programming Under Linear Perturbations: I. Continuity of the Solution Maps?16. Quadratic Programming Under Linear Perturbations: II. Properties of the Optimal Value Function?17. Quadratic Programming Under Linear Perturbations: III. The Convex Case?18. Continuity of the Solution Map in Affine Variational Inequalities?References?Index