Preface.- Part I Background.- 1. Linear Algebra.- 2. Optimization.- Part II Algorithms.- 3. Conjugate Gradients for Unconstrained Minimization.- 4. Equality Constrained Minimization.- 5. Bound Constrained Minimization.- 6. Bound and Equality Constrained Minimization.- Part III Applications to Variational Inequalities.- 7. Solution of a Coercive Variational Inequality by FETI-DP method.- 8. Solution to a Semicoercive Variational Inequality by TFETI Method.- References.- Index.
I Background.- Linear Algebra.- Optimization.- II Algorithms.- Conjugate Gradients for Unconstrained Minimization.- Equality Constrained Minimization.- Bound Constrained Minimization.- Bound and Equality Constrained Minimization.- III Applications to Variational Inequalities.- Solution of a Coercive Variational Inequality by FETI#x2014;DP Method.- Solution of a Semicoercive Variational Inequality by TFETI Method.
Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments.
This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
The first monograph to present the solution to quadratic programming problems, a topic usually addressed only in journal publications
Offers theoretical and practical results in the field of bound-constrained and equality-constrained optimization
Provides algorithms with the rate of convergence independent of constraints
Develops theoretically supported scalable algorithms for variational inequalities
Comprehensive presentation of working set methods and inexact augmented Lagrangians