Global optimization of multiplicative programs
type: Item
instance of: scholarly article
title: Global optimization of multiplicative programs
zbMATH Open document ID: 1052.90091
DOI: 10.1023/A:1024700901538
author: Nikolaos V. Sahinidis
author: Hong Seo Ryoo
published in: Journal of Global Optimization
publication date: 2003-08-21T00:00:00Z
review text: The following two optimization problems are considered: Linear Multiplicative Problem (LMP); Generalized Linear Multiplicative Problem (GLMP). The LMP consists in finding the global minimum of the objective function, which is equal to the product of a finite number of linear functions, under linear constraints; it is assumed that all variables are bounded from below and from above and the linear functions in the objective function are positive over the whole set of feasible soluhons. The GLMP has the same set of feasible solutions as the LMP and its objective function is the sum of a finite number of functions, each of which has the same form as the objective function of the LMP, i.e., it is the product of a finite number of linear functions; unlike to LMP no assumption about the values of the linear functions involved in the objective function of the GMLP is made. The primary contributions of the paper are: (1) Global minimization algorithms that make possible for the first time to solve large-scale LMPs and GMLPs are developed; (2) A new branching scheme that can be used in the context of any rectangular branch-and-bound algorithm is proposed. Extensive computational experiments documenting the advantages of the developed algorithms are reported at the end of the paper.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C57
zbMATH DE Number: 1968920
zbMATH Keywords: Linear Multiplicative Problem
zbMATH Keywords: Generalized Linear Multiplicative Problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1968920