RECENT RESULTS ON SEQUENTIAL OPTIMALITY THEOREMS FOR CONVEX OPTIMIZATION PROBLEMS (Nonlinear Analysis and Convex Analysis)

In this brief note, we review sequential optimality theorems in [5]. We give two kinds of sequential optimality theorems for a convex optimization problem, which are expressed in terms of sequences of epsilon-subgradients and subgradients of involved functions

ON SEMIDEFINITE LINEAR FRACTIONAL OPTIMIZATION PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

Recently, semidefinite optimization problems have been intensively studied since many optimization problems can be changed into the problems and the problems are very tractable ([5]). In this paper, we review the duality results for semidefinite linear fractional optimization problems in the paper ([3] On duality theorems for semidefinite linear fractional optimization problems, Journal of Nonliner and Convex Analysis, volume 20, 2019, 1907-1912)

Optimality and Duality for Multiobjective Fractional Programming Involvingn-Set Functions

AbstractWe consider a multiobjective fractional programming problem (MFP) involving vector-valued objectiven-set functions in which their numerators are different from each other, but their denominators are the same. By using the concept of proper efficiency, we establish optimality conditions and duality relations for our problem (MFP) under convexity assumptions on objective and constrained functions

A general vector-valued variational inequality and its fuzzy extension

A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem

On Set-Valued Complementarity Problems

This paper investigates the set-valued complementarity problems (SVCP) which poses rather different features from those that classical complementarity problems hold, due to tthe fact that he index set is not fixed, but dependent on . While comparing the set-valued complementarity problems with the classical complementarity problems, we analyze the solution set of SVCP. Moreover, properties of merit functions for SVCP are studied, such being as level bounded and error bounded. Finally, some possible research directions are discussed