期刊
SIAM JOURNAL ON OPTIMIZATION
卷 28, 期 2, 页码 1104-1120出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M107534X
关键词
proximal point method; multiobjective optimization; locally Lipschitz function; Pareto critical point; compromise problem; variational rationality
资金
- FAPEG [201210267000909 - 05/2012]
- CNPq [458479/2014-4, 471815/2012-8, 312077/2014-9, 305462/2014-8]
- CAPES [88881.117595/2016-01]
- ANR GREEN-Econ research project [ANR-16-CE03-0005]
- CNPq-Ciencias sem Fronteiras grant [203360/2014-1]
- [MTM2015-65242-C2-1-P]
This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953-970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.
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