Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Mathematical Programming Problems with Equilibrium Constraints on Hadamard Manifolds

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.