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

Yurii Nesterov
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Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium

No 2022015, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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: Structural optimization; self-concordant functions; self-concordant barriers; path-following method; polynomial-time complexity (search for similar items in EconPapers)
Pages: 15
Date: 2022-03-24
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