Coercivity and generalized proximal algorithms: application—traveling around the world

E. A.Papa Quiroz, A. Soubeyran, P. R. Oliveira

Research output: Contribution to journalArticlepeer-review

Abstract

We present an inexact proximal point algorithm using quasi distances to solve a minimization problem in the Euclidean space. This algorithm is motivated by the proximal methods introduced by Attouch et al., section 4, (Math Program Ser A, 137: 91–129, 2013) and Solodov and Svaiter (Set Valued Anal 7:323–345, 1999). In contrast, in this paper we consider quasi distances, arbitrary (non necessary smooth) objective functions, scalar errors in each objective regularized approximation and vectorial errors on the residual of the regularized critical point, that is, we have an error on the optimality condition of the proximal subproblem at the new point. We obtain, under a coercivity assumption of the objective function, that all accumulation points of the sequence generated by the algorithm are critical points (minimizer points in the convex case) of the minimization problem. As an application we consider a human location problem: How to travel around the world and prepare the trip of a lifetime.

Original languageEnglish
Pages (from-to)451-467
Number of pages17
JournalAnnals of Operations Research
Volume321
Issue number1-2
DOIs
StatePublished - Feb 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Coercivity
  • Inexact algorithms
  • Proximal point methods
  • Quasi distances
  • Traveler problem
  • Variational rationality

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