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The main aim of this paper is to investigate weakly/properly/robust efficient solutions of a nonsmooth semi-infinite multiobjective programming problem, in terms of convexificators. In some of the results, we assume the feasible set to be locally star-shaped. The appearing functions are not necessarily smooth/locally Lipschitz/convex. First, constraint qualifications and the normal cone to the feasible set are studied. Then, as a major part of the paper, various necessary and sufficient optimality conditions for solutions of the problem under consideration are presented. The paper is closed by a linear approximation problem to detect the solutions and by studying a gap function. [ABSTRACT FROM PUBLISHER]

In this paper, a new iterative method for finding the projection onto the intersection of two closed convex sets in the framework of Banach spaces is presented. It is a viscosity approximation method which produces a strongly convergent sequence. [ABSTRACT FROM AUTHOR]

This paper aims to solve the joint chance constrained programs (JCCP) by a DC (difference of two convex functions) function approach, which was established by Hong et al. [Oper. Res. 2011;59:617–630]. They used a DC function to approximate the chance constraint functionand constructed a sequential convex approximation method to solve the approximation problem. A disadvantage of this method is perhaps that the DC function they used is nonsmooth. In this article, we first propose a class of smoothing functions to approximate the maximum functionand the indicator function. Then, we construct the conservative smooth DC approximation function toand obtain the smooth DC approximation problems to JCCPs. We show that the solutions of a sequence of smooth approximation problems converge to some Karush–Kuhn–Tucker point of JCCPs under a certain asymptotic regime. [ABSTRACT FROM PUBLISHER]

This paper presents a method for approximating the nondominated set of a multiobjective linear fractional programming (MOLFP) problem. The resulting approximation set has acceptable quality measures, and is an-approximation to the nondominated set, whereis the tolerance vector and can be controlled by the decision-maker. The distance between every two resulting solutions is greater than or equal to a positive valueand hence there is no redundant information. Also, for a given upper bound the method controls the cardinality of the resulting approximation set. [ABSTRACT FROM PUBLISHER]

In this paper, we first discuss the Painlevé–Kuratowski set convergence of (weak) minimal point set for a convex set, when the set and the ordering cone are both perturbed. Next, we consider a convex vector optimization problem, and take into account perturbations with respect to the feasible set, the objective function and the ordering cone. For this problem, by assuming that the data of the approximate problems converge to the data of the original problem in the sense of Painlevé–Kuratowski convergence and continuous convergence, we establish the Painlevé–Kuratowski set convergence of (weak) minimal point and (weak) efficient point sets of the approximate problems to the corresponding ones of original problem. We also compare our main theorems with existing results related to the same topic. [ABSTRACT FROM PUBLISHER]