Proximal point methods for multiobjective optimization in riemannian manifolds

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Dettagli Bibliografici
Autore principale:	Meireles, Lucas Vidal de
Data di pubblicazione:	2019
Natura:	Doctoral thesis
Lingua:	eng
Fonte:	Repositório Institucional da UFG
Download full:	http://repositorio.bc.ufg.br/tede/handle/tede/9410
Riassunto:	In this work, two different proximal-type methods are investigated in the Riemannian context, namely, an exact and an inexact version. Two strategies were used to analyze these methods. For the exact version, we used a direct approach by investigating the regularized problem, not considering any convexity assumption over the constraint sets, that determine the vectorial improvement steps, which replaces the classical approach via scalarization. To study the inexact version, a definition of the approximate Pareto efficient solution is introduced. For the convex case on Hadamard manifolds, full convergence of both methods to a weak Pareto optimal point is obtained.

Descrizione
Riassunto:	In this work, two different proximal-type methods are investigated in the Riemannian context, namely, an exact and an inexact version. Two strategies were used to analyze these methods. For the exact version, we used a direct approach by investigating the regularized problem, not considering any convexity assumption over the constraint sets, that determine the vectorial improvement steps, which replaces the classical approach via scalarization. To study the inexact version, a definition of the approximate Pareto efficient solution is introduced. For the convex case on Hadamard manifolds, full convergence of both methods to a weak Pareto optimal point is obtained.

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