In this paper, we are concerned with a set-valued fractional extremal programming problem under inclusion constraints. Our approach consists of using the extremal principle (an approach initiated by Mordukhovich, which does not involve any convex approximations and convex separation arguments)...

In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend...

In this paper, we first derive several characterizations of the nonemptiness and compactness for the solution set of a convex scalar set-valued optimization problem (with or without cone constraints) in which the decision space is finite-dimensional. The characterizations are expressed in terms...

In the paper, we introduce the concepts of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation>-type I and generalized <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$G$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>G</mi> </math> </EquationSource> </InlineEquation>-type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle...

We consider various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. By using first and second-order approximations as generalized derivatives, we establish both necessary and sufficient optimality conditions. Our first-order conditions are shown to be...

This paper studies a general vector optimization problem which encompasses those related to efficiency, weak efficiency, strict efficiency, proper efficiency and approximate efficiency among others involving non necessarily preordering relations. Based on existing results about complete...

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>

In this paper, we consider a class of mathematical programs governed by second-order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict...