Extending the proximal point algorithm beyond convexity - Archive ouverte HAL
Conference Papers Year : 2022

Extending the proximal point algorithm beyond convexity

Abstract

Introduced in the 1970's by Martinet for minimizing convex functions and extended shortly afterwards by Rockafellar towards monotone inclusion problems, the proximal point algorithm turned out to be a viable computational method for solving various classes of (structured) optimization problems even beyond the convex framework. In this talk we discuss some extensions of proximal point type algorithms beyond convexity. 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, that can be extended to equilibrium functions involving such functions. Computational results confirm the theoretical advances.
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Dates and versions

hal-04005190 , version 1 (26-02-2023)

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  • HAL Id : hal-04005190 , version 1

Cite

Sorin-Mihai Grad, Felipe Lara, Raul Tintaya Marcavillaca. Extending the proximal point algorithm beyond convexity. 2nd International Conference on Nonlinear Applied Analysis and Optimization - ICNAAO & NMD-2022, Tanmoy Som, Dec 2022, Varanasi, India. ⟨hal-04005190⟩
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