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

Yurii Nesterov ()
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Yurii Nesterov: Catholic University of Louvain (UCLouvain)

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 2, 26 pages

Abstract: 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.

Keywords: Convex optimization; Interior-point methods; Self-concordant functions; Polynomial-time methods; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02163-x

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