Nonlinear rescaling and proximal-like methods in convex optimization
Polyak, Roman
Teboulle, Marc

Date: 1997
Abstract: The nonlinear rescaling principle (NRP) consists of transforming the objective function and/or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides. A nonlinear transformation parameterized by a positive scalar parameter and based on a smooth scaling function is used to transform the constraints. The methods based on NRP consist of sequential unconstrained minimization of the classical Lagrangian for the equivalent problem, followed by an explicit formula updating the Lagrange multipliers. We first show that the NRP leads naturally to proximal methods with an entropy-like kernel, which is defined by the conjugate of the scaling function, and establish that the two methods are dually equivalent for convex constrained minimization problems. We then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy-like proximal methods for convex constrained optimization problems. Special cases of the nonlinear rescaling algorithm are presented. In particular a new class of exponential penalty-modified barrier functions methods is introduced.
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió publicada
Subject: Convex optimization ; Nonlinear rescaling ; Modified barrier functions ; Augmented Lagrangians ; Proximal methods
Published in: Mathematical Programming, vol. 76 n. 2 (1997) p. 265-284, ISSN 0025-5610



20 p, 952.0 KB
 UAB restricted access

The record appears in these collections:
Articles > Research articles
Articles > Published articles

 Record created 2006-03-13, last modified 2023-06-03



   Favorit i Compartir