Andreea Mădălina Rusu-Stancu

In this article, we investigate nonsmooth multiobjective mathematical programming problems with equilibrium constraints (NMMPEC) in the framework of Hadamard manifolds. Corresponding to (NMMPEC), the generalized Guignard constraint qualification (GGCQ) is introduced in the Hadamard manifold setting. Further, Karush-Kuhn-Tucker (KKT) type necessary criteria of Pareto-efficiency are derived for (NMMPEC). Subsequently, we introduce several (NMMPEC)-tailored constraint qualifications. We establish several interesting interrelations between these constraint qualifications. Moreover, we deduce that these constraint qualifications are sufficient conditions for (GGCQ). We have furnished non-trivial numerical examples in the setting of some well-known manifolds to illustrate the significance of our results. To the best of our knowledge, constraint qualifications and optimality conditions for (NMMPEC) have not yet been studied in the Hadamard manifold setting.

This article investigates robust optimality conditions and duality results for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (UNMPVC). Mathematical programming problems with vanishing constraints constitute a distinctive class of constrained optimization problems because of the presence of complementarity constraints. Moreover, uncertainties are inherent in various real-life problems. The aim of this article is to identify an optimal solution to an uncertain optimization problem with vanishing constraints that remains feasible in every possible future scenario. Stationary conditions are necessary conditions for optimality in mathematical programming problems with vanishing constraints. These conditions can be derived under various constraint qualifications. Employing the properties of convexificators, we introduce generalized standard Abadie constraint qualification (GS-ACQ) for the considered problem, UNMPVC. We introduce a generalized robust version of nonsmooth stationary conditions, namely a weakly stationary point, a Mordukhovich stationary point, and a strong stationary point (RS-stationary) for UNMPVC. By employing GS-ACQ, we establish the necessary conditions for a local weak Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we derive sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type and Mond–Weir-type robust dual models corresponding to the primal problem, UNMPVC.

This article investigates robust optimality and duality for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (in short, UNMPVC) via convexificators. Using the properties of convexificators, we introduce generalized standard Abadie constraint qualification (in short, GS-ACQ) for the considered problem UNMPVC. Moreover, we introduce generalized robust version of nonsmooth stationary conditions, namely, weakly stationary point (in short, RW-Stationary), T-stationary point (in short, RT-Stationary), M-stationary point (in short, RM-Stationary) and S-stationary point (in short, RS-Stationary) for UNMPVC. By employing GS-ACQ, we establish that the RS-Stationary is the necessary first-order optimality condition for a local Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNMPVC.

We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n -set functions.