In this paper we study the mathematical program with geometric constraints such that the image of a mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the nonsmooth enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. In the case where the Banach space is a weakly compactly generated Asplun...

The capacity of discrete time uncorrelated Rayleigh fading multiple input multiple output (MIMO) channels was investigated without channel state information (CSI) at either the transmitter or the receiver. To achieve the capacity, the amplitude of the multiple input needs to have a discrete distribution with a finite number of mass points with one of them located at the origin. It is shown how ...

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-...

We propose a generalized second-order asymptotic contingent epiderivative of set-valued mapping, study its properties, as well relations to some epiderivatives, and sufficient conditions for existence. Then, using these we investigate optimization problems with inequality constraints. Both necessary optimality the Karush–Kuhn–Tucker type are established under constraint qualification. An applic...

We consider the convex optimization problem minx{f(x) : gj(x) ≤ 0, j = 1, . . . , m} where f is convex, the feasible set K is convex and Slater’s condition holds, but the functions gj ’s are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minim...

Abstract In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification modified qualification, Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization by using nonlinear version Gordan theore...

In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by second-order cones. There are difficulties in applying the classical Karush–Kuhn–Tucker (KKT) condition to the SOCMPCC directly since the usual constrai...

Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, are a difficult class of constrained optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications (CQs). Thus, the Karush-Kuhn-Tucker (KKT) conditions are not necessarily satisfied by minimizers and the convergence assumptions of many meth...

Abstract We consider the class of mathematical programs with orthogonality type constraints. Orthogonality constraints appear by reformulating sparsity constraint via auxiliary binary variables and relaxing them afterwards. For a necessary optimality condition in terms T-stationarity is stated. The justification threefold. First, it allows to capture global structure Morse theory, i. e. deforma...