Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
Language: English
Published by Birkhäuser, Birkhäuser, 2005
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Druck auf Anfrage Neuware - Printed after ordering - Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). Such problems arise in many elds, such as process industry, engineering design, communications, and nance. There is currently a huge gap between MINLP and mixed integer linear programming(MIP) solvertechnology.With a modernstate-of-the-artMIP solver itispossibletosolvemodelswithmillionsofvariablesandconstraints,whereasthe dimensionofsolvableMINLPsisoftenlimitedbyanumberthatissmallerbythree or four orders of magnitude. It is theoretically possible to approximate a general MINLP by a MIP with arbitrary precision. However, good MIP approximations are usually much larger than the original problem. Moreover, the approximation of nonlinear functions by piecewise linear functions can be di cult and ti- consuming. In this book relaxation and decomposition methods for solving nonconvex structured MINLPs are proposed. In particular, a generic branch-cut-and-price (BCP) framework for MINLP is presented. BCP is the underlying concept in almost all modern MIP solvers. Providing a powerful decomposition framework for both sequential and parallel solvers, it made the success of the current MIP technology possible. So far generic BCP frameworks have been developed only for MIP, for example,COIN/BCP (IBM, 2003) andABACUS (OREAS GmbH, 1999). In order to generalize MIP-BCP to MINLP-BCP, the following points have to be taken into account: - A given (sparse) MINLP is reformulated as a block-separable program with linear coupling constraints.The block structure makes it possible to generate Lagrangian cuts and to apply Lagrangian heuristics. - In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed.- The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers. …
Seller Inventory # 9783764372385
- Title
- Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
- Author
- Ivo Nowak
- Publisher
- Birkhäuser, Birkhäuser
- Publication year
- 2005
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3764372389
- ISBN 13
- 9783764372385
- Item weight
- 518 grams
- Dimensions
- 241x160x18 mm
"Synopsis" may belong to another edition of this title.
From the Back Cover
This book presents a comprehensive description of theory, algorithms and software for solving nonconvex mixed integer nonlinear programs (MINLP). The main focus is on deterministic global optimization methods, which play a very important role in integer linear programming, and are used only recently in MINLP.
The presented material consists of two parts. The first part describes basic optimization tools, such as block-separable reformulations, convex and Lagrangian relaxations, decomposition methods and global optimality criteria. Some of these results are presented here for the first time.
The second part is devoted to algorithms. Starting with a short overview on existing methods, deformation, rounding, partitioning and Lagrangian heuristics, and a branch-cut-and-price algorithm are presented. The algorithms are implemented as part of an object-oriented library, called LaGO. Numerical results on several mixed integer nonlinear programs are reported to show abilities and limits of the proposed solution methods.
The book contains many illustrations and an up-to-date bibliography. Because of the emphasis on practical methods, as well as the introduction into the basic theory, it is accessible to a wide audience and can be used both as a research as well as a graduate text.
"About the title" may belong to another edition of this title.
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