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The aim of this paper is to provide a general description of the Pareto subdifferential (weak and proper) of the sum of two cone-convex set-valued mappings in terms of sequences without any constraint qualifications. As an application, we derive sequential Lagrange multipliers optimality conditions for general set-valued optimization problem in terms of sequential Lagrange multipliers at nearby points for the Pareto efficient solutions, where no constraint qualification is assumed. [ABSTRACT FROM AUTHOR]

This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the strong vector subdifferential of the convex set-valued mapping F +GoH, where F; G, and H are convex set-valued mappings, and G is nondecreasing. An application is given to deal with optimality conditions for a constrained convex set-valued optimization problem. [ABSTRACT FROM AUTHOR]

Without any qualification condition, we provide a sequential formula for the ε-subdifferential of multi-composed convex functions via the perturbation theory. As an application of this formula, necessary and sufficient sequential ε-optimality conditions are obtained for the location problems with monotonic gauges. [ABSTRACT FROM AUTHOR]

This paper deals with the subdifferential of convex analysis defined in the Pareto sense, from a point of view of nonvacuity, characterizations, and calculus rules and their applications to the vector optimization, the convex maps being vector-valued in a finite- or infinite-dimensional ordered vector space. Subdifferentiability is characterized under conditions of Attouch-Brézis type. Formulations by derivatives, when they exist, are provided. Concerning the calculus rules, the first main result gives the gap between the Pareto subdifferential and the ordinary one, allowing thus the computation of the one from the other. Next, as central results, Pareto subdifferentials of the sum and/or composition of two convex vector mappings are developed. The formulas are obtained under Moreau-Rockafellar or Attouch-Brézis-type conditions, revealing, strangely, the presence of the ordinary subdifferential. These formulas actually allow the extension of the indicator function technique to the vector case, so that Pareto optimality (efficiency) conditions are easily derived and weakened with qualification conditions of the Attouch-Brézis kind. Finally, the gap between efficient and optimal sets is also deduced. [ABSTRACT FROM AUTHOR]