Skip to main content

Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

Author(s): Misener, Ruth; Floudas, Christodoulos A

Download
To refer to this page use: http://arks.princeton.edu/ark:/88435/pr10563
Abstract: We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to 𝜖 -global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib.htm).
Publication Date: 2012
Citation: Misener, Ruth, and Christodoulos A. Floudas. "Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations." Mathematical Programming 136, no. 1 (2012): 155-182. doi: 10.1007/s10107-012-0555-6
DOI: doi:10.1007/s10107-012-0555-6
ISSN: 0025-5610
EISSN: 1436-4646
Pages: 155 - 182
Type of Material: Journal Article
Journal/Proceeding Title: Mathematical Programming
Version: Author's manuscript



Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.