Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious...

We give a generic regularity condition under which each weakly efficient decision making unit in the CCR model of data envelopment analysis is also CCR-efficient. Then we interpret the problem of finding maximal parameters which preserve efficiency of CCR-efficient DMUs under directional...

LetZ be a compact set of the real space ℜ with at leastn + 2 points;f,h1,h2:Z → ℜ continuous functions,h1,h2 strictly positive andP(x,z),x≔(x 0 ,...,x n ) τ ε ℜ n+1 ,z ε ℜ, a polynomial of degree at mostn. Consider a feasible setM ≔ {x ε ℜ n+1 ∣∀z εZ, −h 2 (z) ≤P(x,...

LetZ be a compact set of the real space ℜ with at leastn + 2 points;f,h1,h2:Z → ℜ continuous functions,h1,h2 strictly positive andP(x,z),x≔(x <Subscript>0</Subscript>,...,x <Subscript> n </Subscript>)<Superscript>τ</Superscript> ε ℜ<Superscript> n+1</Superscript>,z ε ℜ, a polynomial of degree at mostn. Consider a feasible setM ≔ {x ε ℜ<Superscript> n+1</Superscript>∣∀z εZ, −h <Subscript>2</Subscript>(z) ≤P(x,...</subscript></superscript></superscript></superscript></subscript></subscript>

We give a generic regularity condition under which each weakly efficient decision making unit in the CCR model of data envelopment analysis is also CCR-efficient. Then we interpret the problem of finding maximal parameters which preserve efficiency of CCR-efficient DMUs under directional...

This paper aims to study a broad class of generalized semi-infinite programming problems with (upper and lower level) objectives given as the difference of two convex functions, and (lower level) constraints described by a finite number of convex inequalities and a set constraints. First, we are...

Recently, so-called trade-off directions have been introduced for convex multiobjective optimization problems and, later, they have been generalized for nonconvex problems. The trade-off directions are characterized with the help of tangent and contingent cones. Trade-offs give information about...

In this work, by using weak conjugate maps given in (Azimov and Gasimov, in Int J Appl Math 1:171–192, <CitationRef CitationID="CR1">1999</CitationRef>), weak Fenchel conjugate dual problem, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${(D_F^w)}$$</EquationSource> </InlineEquation> , and weak Fenchel Lagrange conjugate dual problem <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${(D_{FL}^w)}$$</EquationSource> </InlineEquation> are constructed. Necessary and sufficient conditions for...</equationsource></inlineequation></equationsource></inlineequation></citationref>

In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two...