research-article

A Proximal Method to Solve Quasiconvex Non-differentiable Location Problems

Authors:

Miguel Angel Cano Lengua,

Erik Alex Papa QuirozAuthors Info & Claims

ICMSSP '20: Proceedings of the 2020 5th International Conference on Multimedia Systems and Signal Processing

Pages 98 - 104

https://doi.org/10.1145/3404716.3404735

Published: 08 July 2020 Publication History

Get Access

Abstract

The location problem is of great interest in order to establish different location demands in the state or private sector. The model of this problem is usually reduced to a mathematical optimization problem. In this paper we present a proximal method to solve location problems where the objective function is quasi-convex and non-differentiable. We prove that the iterations given by the method are well defined and under some assumptions on the objective function we prove the convergence of the method.

References

[1]

K. Arrow, A. Enthoven, Rev. Econometria, 29, 22 (1961)

Google Scholar

[2]

Y. Kannai, J. Math Econ. 4, 56 (1977)

Crossref

Google Scholar

[3]

B. Martinet, Rev. fr. inform. rech. opér., Sér. Verte, 4, 5 (1972)

Google Scholar

[4]

R.T. Rockafellar, Math. Oper. Ress., 1, 20 (1976)

Google Scholar

[5]

O. Guler, SIAM J. Control Optim., 29, 17 (1991)

Digital Library

Google Scholar

[6]

F.Clarke, T. Am. Math. Soc, 205, 16 (1975)

Crossref

Google Scholar

[7]

F. Clarke, Optimization and Nonsmooth Analysis (New York, Wiley (1990))

Crossref

Google Scholar

[8]

F. Navarro, Algunas aplicaciones y extensión del método del subgradiente (These: Universidad Nacional Mayor de San Marcos, 2013).

Google Scholar

Index Terms

A Proximal Method to Solve Quasiconvex Non-differentiable Location Problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Quasiconvex programming and unimodality

Recommendations

Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

In this paper, we propose two interior proximal algorithms inspired by the logarithmic-quadratic proximal method. The first method we propose is for general linearly constrained quasiconvex minimization problems. For this method, we prove global ...
Globally Convergent Inexact Generalized Newton Method for First-Order Differentiable Optimization Problems

Motivated by the method of Martinez and Qi (Ref. 1), we propose in this paper a globally convergent inexact generalized Newton method to solve unconstrained optimization problems in which the objective functions have Lipschitz continuous gradient ...
An Appropriate Subdifferential for Quasiconvex Functions

In this paper we introduce and study a subdifferential that is related to the quasi- convex functions, much as the Fenchel--Moreau subdifferential is related to the convex ones. It is defined for any lower semicontinuous function, through an appropriate ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

ICMSSP '20: Proceedings of the 2020 5th International Conference on Multimedia Systems and Signal Processing

May 2020

112 pages

ISBN:9781450377485

DOI:10.1145/3404716

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

In-Cooperation

Shenzhen University: Shenzhen University

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 08 July 2020

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed limited

Conference

ICMSSP 2020

ICMSSP 2020: 2020 5th International Conference on Multimedia Systems and Signal Processing

May 28 - 30, 2020

Chengdu, China

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

0
Total Citations
30
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Reflects downloads up to 18 Dec 2024

Other Metrics

View Author Metrics

Citations

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Index Terms

Recommendations

Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints

Globally Convergent Inexact Generalized Newton Method for First-Order Differentiable Optimization Problems

An Appropriate Subdifferential for Quasiconvex Functions