Two Optimal Value Functions in Parametric Conic Linear Programming

We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipsc...

Full description

Saved in:
Bibliographic Details
Main Authors Luan, Nguyen Ngoc, Kim, Do Sang, Yen, Nguyen Dong
Format Journal Article
LanguageEnglish
Published 16.12.2020
Subjects
Mathematics - Optimization and Control
Online AccessGet full text
DOI10.48550/arxiv.2012.09330

Cover

More Information
Summary:We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.
DOI:10.48550/arxiv.2012.09330