Extending Linear Conditioning to Convex-Concave Optimization: Finite Convergence of the Proximal Point Algorithm

Noureddine Lehdili () and Abdellatif Moudafi ()
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Noureddine Lehdili: Natixis Bank, ERM - Market and Counterparty Risk Modelling
Abdellatif Moudafi: Aix-Marseille Université, Laboratoire d’Informatique et Systèmes (LIS UMR 7020 CNRS / AMU /UTLN)

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 3, 14 pages

Abstract: Abstract This paper delves into the finite termination of the proximal point algorithm (PPA) within the realm of convex-concave optimization, extending the well-established concept of linear conditioning from convex to convex-concave functions. The study builds on both the foundational work of Auslender and Crouzeix who introduced the concept of well-behaved asymptotically convex functions, and Polyak’s examination of linearly conditioned convex functions also known as functions with a sharp minimum. We give several equivalent definitions of the linear conditioning property and we use them to prove the finite convergence of the proximal point algorithm.

Keywords: Proximal Point Algorithm; Linear conditioning; Convex-concave optimization; Minimization; Sharp minimum; Well-behaved asymptotically convex functions; 49J53; 49K99; 90C25; 49M45; 65C25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02700-w

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