Proximal algorithm with quasidistances for multiobjective quasiconvex minimization in Riemannian manifolds

Quiroz E.A.P.; Rocha R.A.; Oliveira P.; Gregório R. · RAIRO - Operations Research (2023) · DOI: 10.1051/ro/2023101

Resumen

We introduce a proximal algorithm using quasidistances for multiobjective minimization problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason of using quasidistances instead of the classical Riemannian distance comes from the applications in economy, computer science and behavioral sciences, where the quasidistances represent a non symmetric measure. Under some appropriate assumptions on the problem and using tools of Riemannian geometry we prove that accumulation points of the sequence generated by the algorithm satisfy the critical condition of Pareto-Clarke. If the functions are convex then these points are Pareto efficient solutions. © The authors. Published by EDP Sciences, ROADEF, SMAI 2023.

Instituciones: Universidad Nacional Mayor de San Marcos