Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming

Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming

4.11 - 1251 ratings - Source



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€c 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. a€c In order to facilitate the generation of polyhedral relaxations, nonlinear c- vex relaxations are constructed. a€c The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.Heuristic Algorithms for the Unconstrained Binary Quadratic Programming Problem. Technical ... In Proceedings of the 8th Allerton Conference on Circuits and Systems Theory, pages 3a€“12. Benson, S. J. ... AIMMS - The Usera#39;s Guide. Paragonanbsp;...


Title:Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming
Author: Ivo Nowak
Publisher:Springer Science & Business Media - 2006-03-28
ISBN-13:

You must register with us as either a Registered User before you can Download this Book. You'll be greeted by a simple sign-up page.

Once you have finished the sign-up process, you will be redirected to your download Book page.

How it works:
  • 1. Register a free 1 month Trial Account.
  • 2. Download as many books as you like (Personal use)
  • 3. Cancel the membership at any time if not satisfied.


Click button below to register and download Ebook
Privacy Policy | Contact | DMCA