Quadratic Programming and Affine Variational Inequalities A Qualitative Study /

• Main Authors: Lee, Gue Myung (Author), Tam, Nguyen Nang (Author), Yen, Nguyen Dong (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2005.
• Series: Nonconvex Optimization and Its Applications, 78
• Subjects: Mathematics.; Operations research.; Decision making.; Mathematical optimization.; Management science.; Optimization.; Operations Research, Management Science.; Operation Research/Decision Theory.

This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution...

Table of Contents:

• Quadratic Programming Problems
• Existence Theorems for Quadratic Programs
• Necessary and Sufficient Optimality Conditions for Quadratic Programs
• Properties of the Solution Sets of Quadratic Programs
• Affine Variational Inequalities
• Solution Existence for Affine Variational Inequalities
• Upper-Lipschitz Continuity of the Solution Map in Affine Variational Inequalities
• Linear Fractional Vector Optimization Problems
• The Traffic Equilibrium Problem
• Upper Semicontinuity of the KKT Point Set Mapping
• Lower Semicontinuity of the KKT Point Set Mapping
• Continuity of the Solution Map in Quadratic Programming
• Continuity of the Optimal Value Function in Quadratic Programming
• Directional Differentiability of the Optimal Value Function
• Quadratic Programming under Linear Perturbations: I. Continuity of the Solution Maps
• Quadratic Programming under Linear Perturbations: II. Properties of the Optimal Value Function
• Quadratic Programming under Linear Perturbations: III. The Convex Case
• Continuity of the Solution Map in Affine Variational Inequalities.