An inexact scalarization proximal point method for multiobjective quasiconvex minimization in Euclidean spaces
DOI:
https://doi.org/10.15381/pes.v22i1.16125Keywords:
Proximal point method; quasiconvex function; multiobjetive optimization; Clarke subdifferential; Fréchet subdifferentialAbstract
In this paper, we present an inexact scalarized proximal point method to solve unconstrained quasiconvex multiobjective minimization problems defined in Euclidean spaces, where the vector functions are locally Lipschitz. Under some natural assumptions, we prove that the sequence generated by the method is well defined and converges globally. Next, introduzing two error criteria on the method, two variants are obtained, and it is proved that the sequences generated by each one of these variants, converge to a Pareto-Clarke critical point of the problem.
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