A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization

作者：Rocha Rogerio A^*; Oliveira Paulo R; Gregorio Ronaldo M; Souza Michael

来源：Journal of Optimization Theory and Applications, 2016, 171(3): 964-979.

DOI：10.1007/s10957-016-1005-z

• Multi-objective optimization
• Proximal point algorithm
• Weak Pareto solution
• Quasi-distance

In this paper, we present a generalized vector-valued proximal point algorithm for convex and unconstrained multi-objective optimization problems. Our main contribution is the introduction of quasi-distance mappings in the regularized subproblems, which has important applications in the computer theory and economics, among others. By considering a certain class of quasi-distances, that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence generated by our algorithm is bounded and its accumulation points are weak Pareto solutions.

• 出版日期2016-12