Local smooth representations of parametric semiclosed polyhedra with applications to sensitivity in piecewise linear programs
type: Item
instance of: scholarly article
title: Local smooth representations of parametric semiclosed polyhedra with applications to sensitivity in piecewise linear programs
zbMATH Open document ID: 1279.90168
author: Ya Ping Fang
author: Nan-Jing Huang
author: Xiao Qi Yang
published in: Journal of Optimization Theory and Applications
publication date: 2013-02-14T00:00:00Z
review text: The authors establish the equivalence between the representation of a smooth parametric semiclosed polyhedron by half-spaces and its representation by vertices. An application is given to study the sensitivity of a parametric piecewise linear problem. Namely, it is proved that the solution set of a parametric piecewise linear problem can be represented as a finite union of semiclosed polyhedra determined by smooth functions whenever the data of the problem smoothly depend on the parameter.
reviewed by: Dinh The Luc
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 6136252
zbMATH Keywords: parametric semiclosed polyhedron
zbMATH Keywords: piecewise linear program
zbMATH Keywords: sensitivity
zbMATH Keywords: smooth representation
MaRDI profile type: Publication
full work available at URL: s10957-012-0089-3
OpenAlex ID: W1999065700
cites work: Convex Analysis
cites work: Q5817859
cites work: Smooth representation of a parametric polyhedral convex set with application to sensitivity in optimization
cites work: Differentiable selection of optimal solutions in parametric linear programming
cites work: Structure and weak sharp minimum of the Pareto solution set for piecewise linear multiobjective optimization
cites work: The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces
cites work: Pareto solutions of polyhedral-valued vector optimization problems in Banach spaces
cites work: Discontinuous piecewise linear optimization
cites work: Piecewise linear multicriteria programs: the continuous case and its discontinuous generalization
cites work: Q3968042
cites work: Q4503250
cites work: Lipschitz Continuity of the Optimal Value via Bounds on the Optimal Set in Linear Semi-Infinite Optimization
cites work: Stability and Sensitivity of Optimization Problems with First Order Stochastic Dominance Constraints
cites work: Introduction to sensitivity and stability analysis in nonlinear programming
cites work: Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions
cites work: Sensitivity analysis in linear optimization: invariant support set intervals
cites work: Multiparametric linear programming: support set and optimal partition invariancy
cites work: A solution approach to the fixed charge network flow problem using a dynamic slope scaling procedure
cites work: Dynamic slope scaling and trust interval techniques for solving concave piecewise linear network flow problems
cites work: A minimax portfolio selection rule with linear programming solution
cites work: Nonconvex, lower semicontinuous piecewise linear optimization
cites work: Lectures on Polytopes
DOI: 10.1007/S10957-012-0089-3
description: scientific article; zbMATH DE number 6136252