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Set-Limited Functions and Polynomial-Time Interior-Point Methods

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  • Yurii Nesterov

    (Catholic University of Louvain (UCLouvain))

Abstract

In this paper, we revisit some elements of the theory of self-concordant functions. We replace the notion of self-concordant barrier by a new notion of set-limited function, which forms a wider class. We show that the proper set-limited functions ensure polynomial time complexity of the corresponding path-following method (PFM). Our new PFM follows a deviated path, which connects an arbitrary feasible point with the solution of the problem. We present some applications of our approach to the problems of unconstrained optimization, for which it ensures a global linear rate of convergence even in for nonsmooth objective function.

Suggested Citation

  • Yurii Nesterov, 2024. "Set-Limited Functions and Polynomial-Time Interior-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 11-26, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-023-02163-x
    DOI: 10.1007/s10957-023-02163-x
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    References listed on IDEAS

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    1. Geovani N. Grapiglia & Yurii Nesterov, 2019. "Accelerated regularized Newton methods for minimizing composite convex functions," LIDAM Reprints CORE 3058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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