Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
09 December 2019 |
24 December 2019 |
10 March 2020 |
Abstract: Recently, the sequential ε-subdifferential calculus rules have received a great deal of interest from the scientific community (see [1] and [2] and references therein). Indeed, these calculus rules enable us to characterize an ε-optimal solution of a scalar or vector convex programming problems in terms of limits of ε-subgradients at nearby points to the nominal point and without assuming any qualification condition (i.e. regularity condition). In this work, by using an approach based on perturbation theory and without imposing any qualification condition, we establish several sequential formulae for the ε-subdifferential of a multi-composed convex function defined in a reflexive Banach space. As an application of these formulae, necessary and sufficient sequential ε-optimality conditions are obtained for location problems with monotonic gauge.
