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

Rogério A. Rocha (), Paulo R. Oliveira (), Ronaldo M. Gregório () and Michael Souza ()
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Rogério A. Rocha: Federal University of Tocantins
Paulo R. Oliveira: Federal University of Rio de Janeiro
Ronaldo M. Gregório: Rural Federal University of Rio de Janeiro
Michael Souza: Federal University of Ceará

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 3, No 11, 964-979

Abstract: Abstract 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.

Keywords: Multi-objective optimization; Proximal point algorithm; Weak Pareto solution; Quasi-distance; 49M37; 65K05; 65K10; 90C25; 90C29 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-1005-z

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