( , ) ρ Φ − invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

We prove that the notion of KT-invexity for continuous-time nonlinear optimization problem is a necessary and sufficient condition for global optimality of a KarushKuhn-Tucker point.

Let $p$ be a rational prime, let $F$ denote finite, unramified extension of ${{\mathbb {Q}}}_p$ , $K$ the maximal ${{\overline {K}}}$ some fixed algebraic closure and {C}}}_p$ completion . $G_F$ absolute Galois group $A$ an abelian variety defined over with good reduction. Classically, Fontaine integral was seen as Hodge–Tate comparison morphism, i.e. map $\varphi _{A} \otimes 1_{{{\mathbb {C}}...

Convex like properties, without vector space structure are intensively used in the minimax theory Since Ky Fan has proved the first minimax theorem for concave-convexlike functions, several authors have proposed other extensions or generalizations for the convexity. In this paper we propose a survey of the recent studies concerning convexity and invexity in optimization theory. In fact, in the ...

The purpose of this paper is to consider a class of nonsmooth minimax fractional semi-infinite programming problem. Based on the concept of H − tangent derivative, a new generalization of convexity, namely generalized uniform ( , ) H B ρ − invexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by uti...

The concept of d−invexity for functions defined on Riemannian manifolds is introduced. Then, this notion is used to obtain optimality conditions for vector optimization problems on Riemannian manifolds. M.S.C. 2010: 58E17, 90C26.

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.