Projection-based local and global Lipschitz moduli of the optimal value in linear programming

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.This research has been partially supported by Grants PGC2018-097960-B-C21 and PID2020-116694GB-I00 from MICINN, Spain, and ERDF, ‘A way to make Europe,’ European Union

Calmness of the Optimal Value in Linear Programming

This research has been partially supported by grant MTM2014-59179-C2-2-P from MINECO, Spain, and FEDER "Una manera de hacer Europa," European Union

Lipschitz of the Optimal Value in Linear Programming

This research has been partially supported by project MTM2014-59179-C2-2-P and its associated grant BES-2015-073220, both from MINECO, Spain and FEDER, "Una manera de hacer Europa", European Union. The authors wish to thank the referees for their suggestions and comments, which have improved the original version of the paper