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

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