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.

Nonsmooth multiobjective mathematical programming problems with equilibrium constraints (NMMPEC) are studied in this article in the Hadamard manifold setting. In the context of $\left(\mathrm{NMMPEC}\right)$, the generalized Guignard constraint qualification (GGCQ) is formulated within the framework of Hadamard manifolds. Moreover, Karush–Kuhn–Tucker (KKT)-type necessary optimality conditions are derived for $\left(\mathrm{NMMPEC}\right)$. Thereafter, we explore constraint qualifications (CQ) tailored to $\left(\mathrm{NMMPEC}\right)$ in the Hadamard manifold setting. Interrelations between these constraint qualifications are subsequently derived. It is further demonstrated that the proposed constraint qualifications, when satisfied, ensure that GGCQ holds. It is noteworthy that constraint qualifications and optimality conditions for $\left(\mathrm{NMMPEC}\right)$ have not been investigated in the Hadamard manifold setting.