Author: L. F. EscuderoPublisher:
ISBN:
Category :
Languages : en
Pages : 167
Book Description
An Algorithm for Large-scale Quadratic Programming Problems and Its Extensions to the Linearly Constrained Nonlinear Case
Author: L. F. EscuderoOptimal Quadratic Programming Algorithms
Author: Zdenek DostálPublisher: Springer Science & Business Media
ISBN: 0387848061
Category : Mathematics
Languages : en
Pages : 293
Book Description
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.
Optimal Quadratic Programming Algorithms
Author: Zdenek DostálPublisher: Springer
ISBN: 9780387571447
Category : Mathematics
Languages : en
Pages : 0
Book Description
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.
Large-scale Sequential Quadratic Programming Algorithms
Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 98
Book Description
Linear and Nonlinear Optimization
Author: Richard W. CottlePublisher: Springer
ISBN: 1493970550
Category : Business & Economics
Languages : en
Pages : 644
Book Description
This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia
Large-Scale Nonlinear Optimization
Author: Gianni PilloPublisher: Springer Science & Business Media
ISBN: 0387300651
Category : Mathematics
Languages : en
Pages : 297
Book Description
This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
Barrier Methods for Large-scale Quadratic Programming
Author: Stanford University. Department of Operations Research. Systems Optimization LaboratoryPublisher:
ISBN:
Category :
Languages : en
Pages : 142
Book Description
An Algorithm for Structured, Large-Scale Quadratic Programming Problems
Author: Cu Duong HaPublisher:
ISBN:
Category :
Languages : en
Pages : 31
Book Description
An algorithm for structured, large-scale, convex quadratic programming problems is described. The structure of the constraint matrix is block diagonal with a small number of coupling constraints and variables. The algorithm utilizes twice a decomposition procedure that was developed earlier. The first time the decomposition procedure is used to break up the coupling constraints, and the second time it is used to break up the coupling variables. Preliminary computational results are also reported. The block diagonal structure with a small number of coupling constraints and variables usually arises from the formulation of multitime period and multidivision production scheduling and distribution models in large corporations. Each block is concerned with the operation of one division during one time period considered in isolation. The coupling constraints arise from the use of common resources of all divisions or from combining the output of divisions to meet overall demands. The coupling variables represent activities that affect the operation of divisions in more than one time period.
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