‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

In this study, generalized multivalued vector inverse quasi-variational inequality problems are developed, and error bounds obtained in terms of the residual gap function, regularized D-gap function. With help these constraints, one can effectively estimate distances between any feasible point solution set involving inequality.

The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formula...

A general class of variational models with concave priors is considered for obtaining certain sparse solutions, for which nonsmoothness and non-Lipschitz continuity of the objective functions pose significant challenges from an analytical as well as numerical point of view. For computing a stationary point of the underlying variational problem, a Newton-type scheme with provable convergence pro...

In this paper, we consider a vector optimization problem involving locally Lipschitz generalized approximately convex functions and provide several concepts of approximate efficient solutions. We formulate variational inequalities Minty Stampacchia type under the framework Clarke subdifferentials use these as tool to characterize an solution problem.

In this paper, by introducing some new concepts in minimal spaces, we prove a generalized form of the Fan-KKM theorem vector spaces. A class F-implicit variational inequality problems and, as an application is investigated. Moreover, existence for kind under suitable assumptions spaces given.