Constraint Qualifications for Nonsmooth Multiobjective Programming Problems with Switching Constraints on Hadamard Manifolds

In this article, we investigate a class of nonsmooth multiobjective mathematical optimization problems with switching constraints (abbreviated as, (NMMPSC)) in the framework of Hadamard manifolds. Corresponding to (NMMPSC), the generalized Guignard constraint qualification (abbreviated as, (GGCQ)) is introduced in the Hadamard manifold setting. Karush–Kuhn–Tucker (abbreviated as, KKT) type necessary conditions of Pareto efficiency are derived for (NMMPSC). Subsequently, we introduce several other constraint qualifications for (NMMPSC), which turn out to be sufficient conditions for (GGCQ). We have furnished non-trivial illustrative examples to justify the significance of our results. To the best of our knowledge, constraint qualifications for (NMMPSC) have not yet been studied in the Hadamard manifold framework.