Strict convex regularizations, proximal points and augmented lagrangians

Carlos Humes Jr.; Paulo Jose Da Silva E Silva

RAIRO - Operations Research (2010)

  • Volume: 34, Issue: 3, page 283-303
  • ISSN: 0399-0559

Abstract

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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 family of augmented Lagrangian methods for convex constrained optimization, that generalizes the PE+ class presented in [2].

How to cite

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Carlos Humes Jr., and Paulo Jose Da Silva E Silva. "Strict convex regularizations, proximal points and augmented lagrangians." RAIRO - Operations Research 34.3 (2010): 283-303. <http://eudml.org/doc/197784>.

@article{CarlosHumesJr2010,
abstract = { 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 family of augmented Lagrangian methods for convex constrained optimization, that generalizes the PE+ class presented in [2]. },
author = {Carlos Humes Jr., Paulo Jose Da Silva E Silva},
journal = {RAIRO - Operations Research},
keywords = {Proximal points methods; augmented Lagrangians; convex programming.},
language = {eng},
month = {3},
number = {3},
pages = {283-303},
publisher = {EDP Sciences},
title = {Strict convex regularizations, proximal points and augmented lagrangians},
url = {http://eudml.org/doc/197784},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Carlos Humes Jr.
AU - Paulo Jose Da Silva E Silva
TI - Strict convex regularizations, proximal points and augmented lagrangians
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 3
SP - 283
EP - 303
AB - 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 family of augmented Lagrangian methods for convex constrained optimization, that generalizes the PE+ class presented in [2].
LA - eng
KW - Proximal points methods; augmented Lagrangians; convex programming.
UR - http://eudml.org/doc/197784
ER -

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