Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds

This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The generalized Guignard constraint qualification (GGCQ), Abadie constraint qualification (ACQ), and the generalized ACQ (GACQ) are introduced in the framework of Hadamard manifolds for NMOPP using the notion of Clarke subdifferentials. Subsequently, by employing GGCQ and geodesic quasiconvexity assumptions, we establish Karush-Kuhn-Tucker (abbreviated as, KKT)-type necessary criteria of Pareto efficiency for NMOPP. Moreover, we establish that ACQ and GACQ are sufficient criteria for satisfaction of GGCQ. Several nontrivial numerical examples are furnished in manifold settings to demonstrate the validity of the derived results. To the best of our knowledge, this is the first time that ACQ, GACQ, GGCQ, and KKT-type necessary criteria of Pareto efficiency for NMOPP have been studied in manifold setting using Clarke subdifferentials.