Optimal quadratic programming algorithms: with applications to variational inequalities

Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields asdiverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programmingis a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportionalto the number of unknowns. For each algorithm presented, the book details itsclassical predecessor, describes its drawbacks, introduces modifications thatimprove its performance, and demonstrates these improvements through numerical experiments. 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 algorithmsfor variational inequalities INDICE: 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.

• ISBN: 978-0-387-84805-1
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 300
• Fecha Publicación: 01/02/2009
• Nº Volúmenes: 1
• Idioma: Inglés