Global multi-parametric optimal value bounds and solution estimates for separable parametric programs
type: Item
instance of: scholarly article
title: Global multi-parametric optimal value bounds and solution estimates for separable parametric programs
zbMATH Open document ID: 0727.90079
DOI: 10.1007/BF02055203
author: Anthony V. Fiacco
published in: Annals of Operations Research
publication date: 1990-01-01T00:00:00Z
review text: This is a discussion of a parametric method for finding global solutions for nonconvex separable programs. The problem is put in the form \[ \text{ minimize } f(x,\epsilon)=\sum^{n}_{p=1}f_ p(x_ p)\quad s.t.\quad g_ i(x,\epsilon)=\sum^{n}_{p=i}g_{ip}(x_ p)- \epsilon_ i\geq 0;\quad i=1,...,m. \] Upper and lower bounds for the solution are obtained for a specific value of \(\epsilon\), using branch- and-bound methods, leading to a new value for \(\epsilon\), and the process is iterated until a desired tolerance level is attained.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90-08
zbMATH DE Number: 4202046
zbMATH Keywords: global solutions
zbMATH Keywords: nonconvex separable programs
zbMATH Keywords: Upper and lower bounds
zbMATH Keywords: branch-and-bound
reviewed by: Morgan A. Hanson
MaRDI profile type: Publication
cites work: Algorithms for parametric nonconvex programming
cites work: Stability of the solution of definite quadratic programs
cites work: Sensitivity Analysis Procedures for Geometric Programs: Computational Aspects
cites work: Q3946693
cites work: Introduction to sensitivity and stability analysis in nonlinear programming
cites work: Q3932564
cites work: Convexity and concavity properties of the optimal value function in parametric nonlinear programming
cites work: Sensitivity analysis in posynomial geometric programming
cites work: Generalized convexity and concavity of the optimal value function in nonlinear programming
cites work: Inequalities for Stochastic Nonlinear Programming Problems
cites work: Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
cites work: Q3677502
cites work: Generalized equations and their solutions, Part I: Basic theory
cites work: Strongly Regular Generalized Equations
cites work: Solving highly nonlinear convex separable programs using successive approximation
description: scientific article; zbMATH DE number 4202046