On Isolated/Properly Efficient Solutions in Nonsmooth Robust Semi-infinite Multiobjective Optimization

On approximate positively properly efficient solutions in nonsmooth semi-infinite multiobjective optimization problems with data uncertainty

“…Remark 3.2. Theorem 3.1 improves [13, Theorem 3.9], [19,Theorem 3.3], and [26,Theorem 2]. Now, we introduce a concept of the robust ε-quasi (KKT) condition for problem (USIMP) s .…”

“…Theorem 4.4 improves Theorem 4 in[26].Theorem 4.5. (ε−quasi strong robust duality) Let x ∈ C be a robust ε-quasi positively properly efficient solution to problem (USIMP) s such that condition (RCQ) is satisfied at x.…”

“…Before we discuss sufficient condition for a robust ε-quasi positively properly efficient solution of problem (USIMP) s , we introduce the concepts of convexity, which are inspired by [26].…”

“…In addition, optimality conditions and duality for isolated efficient solutions/properly efficient solutions of semi-infinite multiobjective optimization problems were studied in [19,20,21,22,23,24,25]. However, there are few results on isolated efficient solutions/properly efficient solutions for the semi-infinite multiobjective optimization problems with uncertainty data [26]. In addition, since sometimes exact solutions do not exist while the approximate ones do, even in the convex case (see [27,28]), the study of approximate solutions becomes significant from both the theoretical aspect and computational applications.…”

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

“…On the other hand, there were few studies on isolated efficient solutions for various vector optimization problems, the reader can consult [14], [30], [31], and [32]. In 2023, based on the robustness methodology, Pham [29] presented a paper on studying the optimality conditions and duality results of non-smooth semi-infinite multi-objective programming problems under uncertainty wherein the local isolated efficient solutions for such programming problems are considered.…”