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

Author

Listed:
  • 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))

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.

Suggested Citation

  • Noureddine Lehdili & Abdellatif Moudafi, 2025. "Extending Linear Conditioning to Convex-Concave Optimization: Finite Convergence of the Proximal Point Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-14, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02700-w
    DOI: 10.1007/s10957-025-02700-w
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