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Relaxation And Decomposition Methods for Mixed Integer Nonlinear Programming (152) - Couverture rigide
Synopsis
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.
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- ÉditeurBirkhauser Verlag AG
- Date d'édition2005
- ISBN 10 3764372389
- ISBN 13 9783764372385
- ReliureRelié
- Langueanglais
- Nombre de pages213
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics, 152)
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Birkhäuser, 2005
ISBN 10 : 3764372389
ISBN 13 : 9783764372385
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hardcover. Etat : Very Good. Crease on cover*. N° de réf. du vendeur mon0000665231
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Birkhäuser Basel, 2005
ISBN 10 : 3764372389
ISBN 13 : 9783764372385
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents the first branch-cut-and-price algorithm for mixed integer nonlinear programming (MINLP)Several new MINLP cuts based on semidefinite programming, interval-gradients and Bezier polynomials are proposedA description of the MINLP solv. N° de réf. du vendeur 5279639
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
Edité par
Birkhäuser Basel, 2005
ISBN 10 : 3764372389
ISBN 13 : 9783764372385
Neuf
Couverture rigide
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevar iables 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. N° de réf. du vendeur 9783764372385
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Birkhäuser Basel, Birkhäuser Basel Aug 2005, 2005
ISBN 10 : 3764372389
ISBN 13 : 9783764372385
Neuf
Couverture rigide
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 232 pp. Englisch. N° de réf. du vendeur 9783764372385
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (International Series of Numerical Mathematics, 152)
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Springer, Basel, Birkhäuser Basel, Birkhäuser Aug 2005, 2005
ISBN 10 : 3764372389
ISBN 13 : 9783764372385
Neuf
Couverture rigide
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 213 pp. Englisch. N° de réf. du vendeur 9783764372385
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
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Relaxation And Decomposition Methods for Mixed Integer Nonlinear Programming: Vol 152
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