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CONVEX HULL RELAXATION (CHR) FOR CONVEX AND NONCONVEX MINLP PROBLEMS WITH LINEAR CONSTRAINTS

Aykut AhlatÁıoğlu(aahlatci***at***princeton.edu)
Monique Guignard(guignard_monique***at***yahoo.fr)

Abstract: The behavior of enumeration-based programs for solving MINLPs depends at least in part on the quality of the bounds on the optimal value and of the feasible solutions found. We consider MINLP problems with linear constraints. The convex hull relaxation (CHR) is a special case of the primal relaxation (Guignard 1994, 2007) that is very simple to implement. In the convex case, it provides a bound stronger than the continuous relaxation bound, and in all cases it provides good, and often optimal, feasible solutions. We present computational results for QAP, GQAP, MSAP and CDAP instances.

Keywords: mixed integer nonlinear programming; primal relaxation; feasible solution; convex hull; bound

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Combinatorial Optimization (Approximation Algorithms )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Department of OPIM Researh Report, Oct. 2010, the Wharton School, University of Pennsylvania

Download: [PDF]

Entry Submitted: 01/30/2011
Entry Accepted: 01/30/2011
Entry Last Modified: 01/30/2011

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