A. Rufián-Lizana

Invex functions and generalized convexity in multiobjective programming

Martin (Ref. 1) studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Kuhn–Tucker points (depending on the case) remains true if we optimize several objective functions instead of one objective function. To this end, we define accurately stationary points and Kuhn–Tucker optimality conditions for multiobjective programming problems. We see that the Martin results cannot be improved in mathematical programming, because the new types of generalized convexity that have appeared over the last few years do not yield any new optimality conditions for mathematical programming problems.

Calculus for interval-valued functions using generalized Hukuhara derivative and applications

This paper is devoted to studying differential calculus for interval-valued functions by using the generalized Hukuhara differentiability, which is the most general concept of differentiability for interval-valued functions. Conditions, examples and counterexamples for limit, continuity, integrability and differentiability are given. Special emphasis is set to the class F(t)=C.g(t), where C is an interval and g is a real function of a real variable. Here, the emphasis is placed on the fact that F and g do not necessarily share their properties, underlying the extra care that must be taken into account when dealing with interval-valued functions. Two applications of the obtained results are presented. The first one determines a Delta method for interval valued random elements. In the second application a new procedure to obtain solutions to an interval differential equation is introduced. Our results are relevant to fuzzy set theory because the usual fuzzy arithmetic, extension functions and (mathematical) analysis are done on @a-cuts, which are intervals.

Relationships between vector variational-like inequality and optimization problems

Abstract In this paper we will establish the relationships between vector variational-like inequality and optimization problems. We will be able to identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problem, under conditions of pseudo invexity. These conditions are more general those existing in the literature.

Generalized invex monotonicity

Abstract In this paper the generalized invex monotone functions are defined as an extension of monotone functions. A series of sufficient and necessary conditions are also given that relate the generalized invexity of the function θ with the generalized invex monotonicity of its gradient function ∇θ. This new class of functions will be important in order to characterize the solutions of the Variational-like Inequality Problem and Mathematical Programming Problem.

A characterization of weakly efficient points

In this paper, we study a characterization of weakly efficient solutions of Multiobjective Optimization Problems (MOPs). We find that, under some quasiconvex conditions of the objective functions in a convex set of constraints, weakly efficient solutions of an MOP can be characterized as an optimal solution to a scalar constraint problem, in which one of the objectives is optimized and the remaining objectives are set up as constraints. This characterization is much less restrictive than those found in the literature up to now.

Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative

This paper addresses the optimization problems with interval-valued objective function. For this we consider two types of order relation on the interval space. For each order relation, we obtain KKT conditions using of the concept of generalized Hukuhara derivative (

Multiobjective fractional programming with generalized convexity

gH

On invex fuzzy mappings and fuzzy variational-like inequalities

-derivative) for interval-valued functions. The