Volume 34, Number 3, July September 2000
|Page(s)||283 - 303|
|Published online||15 August 2002|
Strict convex regularizations, proximal points and augmented lagrangians
Departemento de Ciência da
Instituto de Matemática e Estatística – Usp,
rua de Matao 1010, Cidade Universitaria, CEP 05315-970
Sao Paulo, SP, Brazil.
2 Research of this author is suported by CNPq and PRONEX, Convênio 76.97.1008.00.
3 Departemento de Matemática Aplicada, Instituto de Matemática e Estatística – USP, rua de Matao 1010, Cidade Universitaria, CEP 05315-970 Sao Paulo, SP, Brazil.
4 Research of this author is suported by FAPESP - Processo 96/09939-0.
Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau , 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 family of augmented Lagrangian methods for convex constrained optimization, that generalizes the PE+ class presented in .
Key words: Proximal points methods / augmented Lagrangians / convex programming.
© EDP Sciences, 2000
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