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Rescaled proximal methods for linearly constrained convex problems

Paulo J.S. Silva;  Carlos Humes — 2007

RAIRO - Operations Research

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient...

Strict convex regularizations, proximal points and augmented lagrangians

Carlos Humes Jr.;  Paulo Jose Da Silva E Silva — 2010

RAIRO - Operations Research

Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau [16], Martinet [14, 15] and Rockafellar [19, 20] who used as regularization function the square of the Euclidean norm. In this work, we study PPM in the context of optimization and we derive a class of such methods which contains Rockafellar's result. We also present a less stringent criterion to the acceptance of an approximate solution to the subproblems that arise in the inner loops of PPM. Moreover, we introduce a new...

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