Karush-Kuhn-Tucker Necessary Optimality Conditions for (h, φ)ɛ-Multiobjective Optimization Problems Based on Pseudo-Avriel-Ben-Tal Algebraic Operations

In this paper it is introduced a new generalized pseudo-operation with one parameter of the following form: x ⊕_ɛ y = h⁻¹(h(x) + ɛh(y)), where h is an n vector-valued continuous function, defined on a subset H of ℝⁿ and possessing an inverse function h⁻¹, ɛ is an arbitrary but fixed positive real number. Five kinds of cones are introduced, which are used to establish the constraint qualifications. The generalized Karush-Kuhn-Tucker necessary optimality conditions are developed for a class of generalized (h, φ)_ɛ-differentiable single-objective programming problems and then for multiobjective programming problems, by using this generalized pseudo-operations, an extension of Avriel-Ben-Tal algebraic operations. The results obtained in this paper generalize and extend previous results obtained in this field. At the same time, in the final chapter, a cryptographic application using Ben-Tal type operators is presented.