C. S. Lalitha

Generalized B-vex functions and generalized B-vex programming

A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.

Second order symmetric duality in multiobjective programming

Abstract A pair of Mond–Weir type multiobjective second order symmetric dual programs are formulated without non-negativity constraints. Weak duality, strong duality and converse duality theorems are established under η -bonvexity and η -pseudobonvexity assumptions. A second order self-duality theorem is given by assuming the functions involved to be skew-symmetric.

Vector variational inequalities with cone-pseudomonotone bifunctions

In this article, two types of cone-pseudomonotone bifunctions have been introduced and the weaker form of pseudomonotonicity is used to establish an existence theorem for a Stampacchia-kind vector variational inequality problem given in terms of bifunctions. For a vector optimization problem, the necessary and sufficient optimality conditions in terms of an associated vector variational inequality problem have been established using a generalized form of cone pseudoconvexity of objective function.

Regularity Conditions and Optimality in Vector Optimization

Abstract The aim of this article is to study necessary optimality conditions for a vector minimization program involving locally Lipschitz functions under certain general regularity conditions. We study problems involving only inequality and both inequality and equality constraints.

Generalized Nonsmooth Invexity

Abstract In this paper sufficient optimality conditions and duality results are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke’s generalized gradient is used to define invexity, pβeudoinvexity and quasiinvexity for Lipβchitz functions.

Optimality conditions in convex optimization revisited

The phrase convex optimization refers to the minimization of a convex function over a convex set. However the feasible convex set need not be always described by convex inequalities. In this article we consider a convex feasible set which is described by inequality constraints that are locally Lipschitz and not necessarily convex or differentiable. We show that if the Slater constraint qualification and a simple non-degeneracy condition is satisfied then the Karush–Kuhn–Tucker type optimality condition is both necessary and sufficient.

Stability of Parametric Quasivariational Inequality of the Minty Type

In this paper, stability of a parametric quasivariational inequality of the Minty type is studied via various sufficient conditions characterizing upper and lower semicontinuity of the solution sets as well as the approximate solution sets. Sufficient conditions ensuring upper semicontinuity of the approximate solution sets of an optimization problem with quasivariational inequality constraints are also presented.

Gap functions for vector variational inequalities

In this article, we intend to study several scalar-valued gap functions for Stampacchia and Minty-type vector variational inequalities. We first introduce gap functions based on a scalarization technique and then develop a gap function without any scalarizing parameter. We then develop its regularized version and under mild conditions develop an error bound for vector variational inequalities with strongly monotone data. Further, we introduce the notion of a partial gap function which satisfies all, but one of the properties of the usual gap function. However, the partial gap function is convex and we provide upper and lower estimates of its directional derivative.

Stability for Properly Quasiconvex Vector Optimization Problem

The aim of this paper is to study the stability aspects of various types of solution set of a vector optimization problem both in the given space and in its image space by perturbing the objective function and the feasible set. The Kuratowski–Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set of the original problem is established assuming the objective functions to be (strictly) properly quasi cone-convex.

OPTIMALITY CRITERIA IN SET-VALUED OPTIMIZATION

The main aim of this paper is to obtain optimality conditions for a constrained set-valued optimization problem. The concept of Clarke epiderivative is introduced and is used to derive necessary optimality conditions. In order to establish sufficient optimality criteria we introduce a new class of set-valued maps which extends the class of convex set-valued maps and is different from the class of invex set-valued maps.