Convergence analysis of a generalized proximal algorithm for multiobjective quasiconvex minimization on Hadamard manifolds

In this paper, we introduce a generalized inexact scalarized proximal point algorithm to find Pareto-Clarke critical points and Pareto efficient solutions of quasiconvex multivalued functions defined on Hadamard manifolds considering vectorial and scalar errors to find a critical point of the regularized proximal function in each iteration. Under some assumptions on the problem, we obtain the global convergence of the sequence to a Pareto-Clarke critical point and assuming an extra condition on the proximal parameters we establish convergence to a Pareto efficient solution, approximately linear/superlinear rate of convergence and finite termination of the algorithm. In the convex case, we prove the convergence to a Pareto efficient solution point (more than a weak Pareto efficient solution point). The results of the paper are new even in the Euclidean space.