A Primal-Dual Interior-Point Method for Nonconvex Optimization with Multiple Logarithmic Barrier Parameters and with Strong Convergence Properties

Abstract

It is observed that an algorithm proposed in the 1980s for thesolution of nonconvex constrained optimization problems is in fact aprimal-dual logarithmic barrier interior-point method closely related tomethods under current investigation in the research community. Its maindistinguishing features are judicious selection and update of the multiplebarrier parameters (one per constraint), use of the objective function asmerit function, and careful bending of the search direction. As a payoff,global convergence and fast local convergence ensue. The purpose of thisshort note is to describe the algorithm in the interior-point framework andlanguage and to provide a preliminary numerical evaluation. The latter showsthat the method compares well with algorithms recently proposed by otherresearch groups.