Relaxed-inertial proximal point type algorithms for quasiconvex minimization

S. M. Grad; F. Lara; R. T. Marcavillaca

doi:10.1007/s10898-022-01226-z

Relaxed-inertial proximal point type algorithms for quasiconvex minimization

S. M. Grad
, F. Lara
, R. T. Marcavillaca

Institute of Higher Research

Unité de Mathématiques Appliquées
Corvinus University of Budapest
Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We propose a relaxed-inertial proximal point type algorithm for solving optimization problems consisting in minimizing strongly quasiconvex functions whose variables lie in finitely dimensional linear subspaces. A relaxed version of the method where the constraint set is only closed and convex is also discussed, and so is the case of a quasiconvex objective function. Numerical experiments illustrate the theoretical results.

Original language	English
Pages (from-to)	615-635
Number of pages	21
Journal	Journal of Global Optimization
Volume	85
Issue number	3
DOIs	https://doi.org/10.1007/s10898-022-01226-z
State	Published - Mar 2023

Keywords

Generalized convexity
Inertial methods
Proximal point algorithms
Relaxed methods
Strong quasiconvexity

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10.1007/s10898-022-01226-z

Cite this

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title = "Relaxed-inertial proximal point type algorithms for quasiconvex minimization",

abstract = "We propose a relaxed-inertial proximal point type algorithm for solving optimization problems consisting in minimizing strongly quasiconvex functions whose variables lie in finitely dimensional linear subspaces. A relaxed version of the method where the constraint set is only closed and convex is also discussed, and so is the case of a quasiconvex objective function. Numerical experiments illustrate the theoretical results.",

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note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Lara, F.

AU - Marcavillaca, R. T.

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N2 - We propose a relaxed-inertial proximal point type algorithm for solving optimization problems consisting in minimizing strongly quasiconvex functions whose variables lie in finitely dimensional linear subspaces. A relaxed version of the method where the constraint set is only closed and convex is also discussed, and so is the case of a quasiconvex objective function. Numerical experiments illustrate the theoretical results.

AB - We propose a relaxed-inertial proximal point type algorithm for solving optimization problems consisting in minimizing strongly quasiconvex functions whose variables lie in finitely dimensional linear subspaces. A relaxed version of the method where the constraint set is only closed and convex is also discussed, and so is the case of a quasiconvex objective function. Numerical experiments illustrate the theoretical results.

KW - Generalized convexity

KW - Inertial methods

KW - Proximal point algorithms

KW - Relaxed methods

KW - Strong quasiconvexity

UR - https://www.scopus.com/pages/publications/85137061853

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EP - 635

JO - Journal of Global Optimization

JF - Journal of Global Optimization

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ER -

Relaxed-inertial proximal point type algorithms for quasiconvex minimization

Abstract

Keywords

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