integer nonlinear programming (41 Ergebnisse)

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Buch. Zustand: 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.

Buch. Zustand: Neu. Neuware -It is not an exaggeration that much of what people devote in their hfe re solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 464 pp. Englisch.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - It is not an exaggeration that much of what people devote in their hfe re solves around optimization in one way or another. On one hand, many decision making problems in real applications naturally result in optimization problems in a form of integer programming. On the other hand, integer programming has been one of the great challenges for the optimization research community for many years, due to its computational difficulties: Exponential growth in its computational complexity with respect to the problem dimension. Since the pioneering work of R. Gomory [80] in the late 1950s, the theoretical and methodological development of integer programming has grown by leaps and bounds, mainly focusing on linear integer programming. The past few years have also witnessed certain promising theoretical and methodological achieve ments in nonlinear integer programming. When the first author of this book was working on duality theory for n- convex continuous optimization in the middle of 1990s, Prof. Douglas J. White suggested that he explore an extension of his research results to integer pro gramming. The two authors of the book started their collaborative work on integer programming and global optimization in 1997. The more they have investigated in nonlinear integer programming, the more they need to further delve into the subject. Both authors have been greatly enjoying working in this exciting and challenging field.

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First edition hard back binding in publisher's original burgundy cloth covers, gilt title and author lettering to the spine. 8vo. 9½'' x 6¼''. Contains 544 printed pages of text with monochrome mathematical formulae throughout. Fine condition book in Fine condition dust wrapper, not price clipped. Dust wrapper supplied in archive acetate film protection. Member of the P.B.F.A. ISBN 720420369 PHYSICS.

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