We present an algorithm to solve: Find (x, y) E A A-L such that y Tx, where A is a subspace and T is a maximal monotone operator. The algorithm is based on the proximal decomposition on the graph of a monotone operator and we show how to recover Spingarn's decomposition method. We give a proof of convergence that does not use the concept of partial inverse and show how to choose a scaling factor to accelerate the convergence in the strongly monotone case. Numerical results performed on quadratic problems confirm the robust behaviour of the algorithm.
Publié le : 1995-07-04
Classification:
proximal point algorithm,
partial inverse,
convex programming AMS subject classification 90C25,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-01644645,
author = {Mahey, Philippe and Oualibouch, Said and Pham Dinh , Tao},
title = {PROXIMAL DECOMPOSITION ON THE GRAPH OF A MAXIMAL MONOTONE OPERATOR*},
journal = {HAL},
volume = {1995},
number = {0},
year = {1995},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01644645}
}
Mahey, Philippe; Oualibouch, Said; Pham Dinh , Tao. PROXIMAL DECOMPOSITION ON THE GRAPH OF A MAXIMAL MONOTONE OPERATOR*. HAL, Tome 1995 (1995) no. 0, . http://gdmltest.u-ga.fr/item/hal-01644645/