On the use of cuts in reverse convex programs
type: Item
instance of: scholarly article
title: On the use of cuts in reverse convex programs
zbMATH Open document ID: 0699.90085
DOI: 10.1007/BF00941567
author: T. R. Gurlitz
author: Stephen E. Jacobsen
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: A cutting method, using the idea of Tuy cuts, has been suggested in earlier papers as a possible means of solving reverse convex programs. However, the method is fraught with theoretical and numerical difficulties. Stringent sufficient conditions for convergence in n dimensions are given. However, examples of nonconvergence are given and reasons for this nonconvergence are developed. A result of the discussion is a convergent algorithm which combines the idea of the cutting plane method with vertex enumeration procedures in order to numerically improve upon the edge search procedure of \textit{R. J. Hillestad} [see Oper. Res. 23, 1091-1098 (1975; Zbl 0335.90039)].
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90-08
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4147873
zbMATH Keywords: nonconvex programming
zbMATH Keywords: cutting method
zbMATH Keywords: Tuy cuts
zbMATH Keywords: reverse convex programs
zbMATH Keywords: examples of nonconvergence
zbMATH Keywords: vertex enumeration
MaRDI profile type: Publication
cites work: Iterative Solution of Nonlinear Optimal Control Problems
cites work: Complementary Geometric Programming
cites work: The design centering problem as a d.c. programming problem
cites work: The Validity of a Family of Optimization Methods
cites work: Q5684520
cites work: Characterization of local solutions for a class of nonconvex programs
cites work: An algorithm for optimizing network flow capacity under economies of scale
cites work: Optimization Problems Subject to a Budget Constraint with Economies of Scale
cites work: Reverse convex programming
cites work: Q5342287
cites work: Convex programs with an additional reverse convex constraint
cites work: Methods for Global Concave Minimization: A Bibliographic Survey
cites work: Nondifferentiable reverse convex programs and facetial convexity cuts via a disjunctive characterization
cites work: Convex programs with several additional reverse convex constraints
cites work: Q3730359
cites work: Linear programs with an additional reverse convex constraint
cites work: An algorithm for determining all extreme points of a convex polytope
description: scientific article; zbMATH DE number 4147873