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Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming


Canovas, M J; Gisbert, M J; Klatte, Diethard; Parra, J (2022). Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming. Journal of Optimization Theory and Applications, 193(1-3):280-299.

Abstract

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

Abstract

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
510 Mathematics
Scopus Subject Areas:Social Sciences & Humanities > Management Science and Operations Research
Physical Sciences > Control and Optimization
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied Mathematics, Management Science and Operations Research, Control and Optimization
Language:English
Date:1 June 2022
Deposited On:24 Jan 2023 07:53
Last Modified:28 Feb 2024 02:45
Publisher:Springer
ISSN:1573-2878
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1007/s10957-021-01948-2
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)