Buch, Englisch, Band 152, 213 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 518 g
Buch, Englisch, Band 152, 213 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 518 g
Reihe: International Series of Numerical Mathematics
ISBN: 978-3-7643-7238-5
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Programmierung: Methoden und Allgemeines
- Mathematik | Informatik EDV | Informatik Informatik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
Weitere Infos & Material
Basic Concepts.- Problem Formulations.- Convex and Lagrangian Relaxations.- Decomposition Methods.- Semidefinite Relaxations.- Convex Underestimators.- Cuts, Lower Bounds and Box Reduction.- Local and Global Optimality Criteria.- Adaptive Discretization of Infinite Dimensional MINLPs.- Algorithms.- Overview of Global Optimization Methods.- Deformation Heuristics.- Rounding, Partitioning and Lagrangian Heuristics.- Branch-Cut-and-Price Algorithms.- LaGO — An Object-Oriented Library for Solving MINLPs.
