Proximal algorithm with quasidistances for multiobjective quasiconvex minimization in Riemannian manifolds

¹ Universidad Nacional Mayor de San Marcos, Universidad Privada del Norte, Lima, Peru
² Universidade Federal de Goiás, Goiânia, Brazil
³ Universidade Federal do Tocantins, Palmas, Brazil
⁴ Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
⁵ Universidade Federal Rural do Rio de Janeiro, Rio de Janeiro, Brazil

^* Corresponding author: erikpapa@gmail.com

Received: 31 March 2023
Accepted: 13 July 2023

Abstract

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.