We study a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related arising recent years. To solve this we revisit the Bregman proximal point algorithm (BPPA) introduce new inexact stopping condition for solving subproblems, can circumvent underlying feasibility difficulty often appearing existing cond...

In this paper we introduce a definition of approximate Pareto efficient solution as well necessary condition for such solutions in the multiobjective setting on Riemannian manifolds. We also propose an inexact proximal point method nonsmooth optimization context by using notion solution. The main convergence result ensures that each cluster (if any) any sequence generated is critical point. Fur...

This paper is devoted to the study of the proximal point algorithm for solving monotone second-order cone complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point algorithm ...

This paper deals with the generalized regularization proximal point method which was introduced by the authors in [Four parameter proximal point algorithms, Nonlinear Anal. 74 (2011), 544-555]. It is shown that sequences generated by it converge strongly under minimal assumptions on the control parameters involved. Thus the main result of this paper unify many results related to the prox-Tikhon...