On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

Strict Benson proper-ε-efficiency in vector optimization with set-valued maps

In this paper the notion of Strict Benson proper-?-efficient solution for a vector optimization problem with set-valued maps is introduced. The scalarization theorems and ?-Lagrangian multiplier theorems are established under the assumption of ic-cone-convexlikeness of set-valued maps.

Duality of(h,φ)-Multiobjective Programming Involving Generalized Invex Functions

In the setting of Ben-Tal's generalized algebraic operations, this paper deals with Mond-Weir type dual theorems of multiobjective programming problems involving generalized invex functions. Two classes of functions, namely,(h,φ)-pseudoinvex and(h,φ)-quasi-invex, are defined for a vector function. By utilizing these two classes of functions, some dual theorems are established for conditionally proper efficient solution in(h,φ)-multiobjective programming problems.