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...

In non-regular problems the classical optimality conditions are totally inapplicable. Meaningful results were obtained for problems with conic constraints by Izmailov and Solodov (SIAM J Control Optim 40(4):1280–1295, <CitationRef CitationID="CR17">2001</CitationRef>). They are based on the so-called 2-regularity condition of the...</citationref>

A function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${f : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> , where Ω is a convex subset of the linear space X, is said to be d.c. (difference of convex) if f =  g − h with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${g, h : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> convex functions. While d.c. functions find various applications, especially in optimization, the...</equationsource></inlineequation></equationsource></inlineequation>