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

E. A. Papa Quiroz (), Antoine Soubeyran and P. R. Oliveira ()
Additional contact information
E. A. Papa Quiroz: Universidad Nacional Mayor de San Marcos
P. R. Oliveira: Federal University of Rio de Janeiro

Annals of Operations Research, 2023, vol. 321, issue 1, No 17, 467 pages

Abstract: 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.

Keywords: Proximal point methods; Inexact algorithms; Coercivity; Quasi distances; Variational rationality; Traveler problem (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-022-04725-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: Coercivity and generalized proximal algorithms: application—traveling around the world (2023)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:321:y:2023:i:1:d:10.1007_s10479-022-04725-0

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-022-04725-0

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().