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

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

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
Publication status	Published - 1 Mar 2023

Keywords

Generalized convexity
Inertial methods
Proximal point algorithms
Relaxed methods
Strong quasiconvexity

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10.1007/s10898-022-01226-z

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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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AU - Lara, F.

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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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ER -

Relaxed-inertial proximal point type algorithms for quasiconvex minimization

Abstract

Keywords

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