30 research outputs found
On duality for nonsmooth Lipschitz optimization problems
We present some duality theorems for a non-smooth Lipschitz vector optimization problem. Under generalized invexity assumptions on the functions the duality theorems do not require constraint qualifications
Rated Extremal Principles for Finite and Infinite Systems
In this paper we introduce new notions of local extremality for finite and
infinite systems of closed sets and establish the corresponding extremal
principles for them called here rated extremal principles. These developments
are in the core geometric theory of variational analysis. We present their
applications to calculus and optimality conditions for problems with infinitely
many constraints
Some relationships among the constraint qualifications for Lagrangian dualities in DC infinite optimization problems
Closed convex sets of Motzkin and generalized Minkowski types
The aim of this paper is twofold. On one hand the generalized Minkowski sets
are defined and characterized. On the other hand, the Motzkin decomposable
sets, along with their epigraphic versions are considered and characterized in
new ways. Among them, the closed convex sets with one single minimal face, i.e.
translated closed convex cones, along with their epigraphic counterparts are
particularly studied
Stability of the Duality Gap in Linear Optimization
In this paper we consider the duality gap function g that measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, considering seven different scenarios. In particular we find some stability results by proving that, under mild conditions, either the duality gap of the perturbed problems is zero or + ∞ around the given data, or g has an infinite jump at it. We also give conditions guaranteeing that those data providing a finite duality gap are limits of sequences of data providing zero duality gap for sufficiently small perturbations, which is a generic result.This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-01 and SECTyP-UNCuyo Res. 4540/13-R