TY  - BOOK
AU  - Dostál,Zdenek
ED  - SpringerLink (Online service)
TI  - Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities 
T2  - Springer Optimization and Its Applications,
SN  - 9780387848068
PY  - 2009///
CY  - Boston, MA
PB  - Springer US
KW  - MATHEMATICS
KW  - NUMERICAL ANALYSIS
KW  - MATHEMATICAL OPTIMIZATION
KW  - OPERATIONS RESEARCH
KW  - ENGINEERING MATHEMATICS
KW  - APPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING
KW  - OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
KW  - CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
N1  - 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-DP Method -- Solution of a Semicoercive Variational Inequality by TFETI Method
N2  - 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 as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is 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 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 reader is required to have a basic knowledge of calculus in several variables and linear algebra
UR  - http://dx.doi.org/10.1007/b138610
ER  -