On the need for hybrid steps in hybrid proximal point methods

Authors:
O.Rolando GáRciga;Alfredo Iusem;B. F. Svaiter
Affiliations:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil;Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil;Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil
Venue:
Operations Research Letters
Year:
2001

Citing 2
Cited 1

On the convergence of the proximal point algorithm for convex minimization

SIAM Journal on Control and Optimization
An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions

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Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization

Mathematics of Operations Research

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Abstract

We show that the hybrid steps on the hybrid proximal point methods, allowing for constant relative errors, are necessary in order to ensure boundedness of the iterates, even in the optimization case. Moreover, we show that such conditions do not imply that the sequence of errors becomes summable ''a posteriori''.