A nonsmooth multiobjective optimization problem involving generalized (F, α, ρ, d)-type I function is considered. Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Duality results are...

A real-valued function f defined on a convex subset D of some normed linear space is said to be inner γ-convex w.r.t. some fixed roughness degree γ    0 if there is a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\nu \in]0, 1]$$</EquationSource> </InlineEquation> such that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\rm sup}_{\lambda\in[2,1+1/\nu]} \left(f((1 - \lambda)x_0 + \lambda x_1) - (1 - \lambda) f...</equationsource></inlineequation></equationsource></inlineequation>

A nonsmooth multiobjective optimization problem involving generalized (F, α, ρ, d)-type I function is considered. Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Duality results are...

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$f:X\times Y\to{\mathbb{R}}$$</EquationSource> </InlineEquation> is...</equationsource></inlineequation>

This paper attempts to underline how the Diagonal Transfer Continuity hypothesis (Baye, Tian and Zhou, 1993) and Better-Reply Security (Reny, 1999) are unconnected between themselves as sucient conditions for stating the existence of Nash equilibria. Besides, various examples and counterexamples...

To give sucient conditions for Nash Equilibrium existence in a continuous game is a central problem in Game Theory. In this paper, we present two games in which we show how the continuity and quasi-concavity hypotheses are unconnected one to each other. Then, we relax the quasiconcavity...

The problem of optimizing a biconvex function over a given (bi)convex or compact set frequently occurs in theory as well as in industrial applications, for example, in the field of multifacility location or medical image registration. Thereby, a function $$f:X\times Y\to{\mathbb{R}}$$ is called...

In this paper we introduce several classes of generalized convexfunctions already discussed in the literature and show the relationbetween those function classes. Moreover, for some of those functionclasses a Farkas-type theorem is proved. As such this paper unifiesand extends results existing...

In this paper we introduce several classes of generalized convexfunctions already discussed in the literature and show the relationbetween those function classes. Moreover, for some of those functionclasses a Farkas-type theorem is proved. As such this paper unifiesand extends results existing...