Robust optimality, duality and saddle points for multiobjective fractional semi-infinite optimization with uncertain data

Abstract

This paper is devoted to the investigation of a class of uncertain multiobjective fractional semi-infinite optimization problems (UMFP, for brevity). We first obtain, by combining robust optimization and scalarization methodologies, necessary and sufficient optimality conditions for robust approximate weakly efficient solutions of (UMFP). Then, we introduce a Mixed type approximate dual problem for (UMFP) and investigate their robust approximate duality relationships. Moreover, we obtain some robust approximate weak saddle point theorems for an uncertain multiobjective Lagrangian function related to (UMFP).

Research on power system flexibility considering uncertainties

“…In model (1), the corresponding parameters of both constraints and objective function are determined. However, due to the emergence of various uncertain factors, the problems related to power systems have changed from traditional certainty to uncertainty, and the general expression of the uncertain optimization mathematical model is as follows (Sun et al, 2022):…”

On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems

“…Now, we consider the concept of robust -quasi efficient solution for (UFP). We refer the readers to [19,21,37] for other kinds of robust approximate efficient solutions.…”

“…Antczak [36] establish a new parametric approach for robust approximate quasi-efficient solutions of robust fractional multi-objective optimization problems. Feng and Sun [37] obtain some new results for robust weakly -efficient solutions for an uncertain fractional multi-objective semi-infinite optimization by employing conjugate analysis. Very recently, by employing robust limiting constraint qualification conditions and generalized convexity assumptions, Thuy and Su [38] consider optimality conditions and duality results for nonsmooth fractional multi-objective semi-infinite optimization problems with uncertain data.…”

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

“…Recently, optimality conditions and duality for semi-infinite multiobjective optimization problems have been considered by numerous researchers; see, e.g., [1,2,3,4,5,6,7] and the references therein. For semi-infinite multiobjective optimization problems with data uncertainty; we refer to, for example, [8,9,10,11,12] and the references therein. For isolated efficient solutions and properly efficient solutions for multiobjective optimization problems, we refer to [13,14,15,16,17,18] and the references therein.…”