A **-algorithm for convex minimization

Authors:
Robert Mifflin;Claudia Sagastizábal
Affiliations:
Department of Mathematics, Washington State University, 99164-3113, Pullman, WA, USA;IMPA, Estrada Dona Castorina 110, Jardim Botânico, 22460-320, Rio de Janeiro, RJ, Brazil
Venue:
Mathematical Programming: Series A and B
Year:
2005

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Abstract

For convex minimization we introduce an algorithm based on **-space decomposition. The method uses a bundle subroutine to generate a sequence of approximate proximal points. When a primal-dual track leading to a solution and zero subgradient pair exists, these points approximate the primal track points and give the algorithm's **, or corrector, steps. The subroutine also approximates dual track points that are **-gradients needed for the method's **-Newton predictor steps. With the inclusion of a simple line search the resulting algorithm is proved to be globally convergent. The convergence is superlinear if the primal-dual track points and the objective's **-Hessian are approximated well enough.