# A generalized proximal point algorithm for the nonlinear complementarity problem

Regina S. Burachik; Alfredo N. Iusem

RAIRO - Operations Research (2010)

- Volume: 33, Issue: 4, page 447-479
- ISSN: 0399-0559

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topBurachik, Regina S., and Iusem, Alfredo N.. "A generalized proximal point algorithm for the nonlinear complementarity problem ." RAIRO - Operations Research 33.4 (2010): 447-479. <http://eudml.org/doc/197803>.

@article{Burachik2010,

abstract = {
We consider a generalized proximal point method (GPPA) for
solving the nonlinear complementarity problem with monotone operators in
Rn. It differs from the classical proximal point method discussed
by Rockafellar for the problem of finding zeroes of monotone operators
in the use of generalized distances, called φ-divergences,
instead of the Euclidean one. These distances play not only a
regularization role but also a penalization one, forcing the sequence
generated by the method to remain in the interior of the feasible set,
so that the method behaves like an interior point one. Under appropriate
assumptions on the φ-divergence and the monotone operator we
prove that the sequence converges if and only if the problem has
solutions, in which case the limit is a solution. If the problem does
not have solutions, then the sequence is unbounded. We extend previous
results for the proximal point method concerning convex optimization
problems.
},

author = {Burachik, Regina S., Iusem, Alfredo N.},

journal = {RAIRO - Operations Research},

keywords = { Nonlinear complementarity problem; proximal point methods;
monotone operators.
; nonlinear complementarity problem; monotone operators},

language = {eng},

month = {3},

number = {4},

pages = {447-479},

publisher = {EDP Sciences},

title = {A generalized proximal point algorithm for the nonlinear complementarity problem },

url = {http://eudml.org/doc/197803},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Burachik, Regina S.

AU - Iusem, Alfredo N.

TI - A generalized proximal point algorithm for the nonlinear complementarity problem

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 4

SP - 447

EP - 479

AB -
We consider a generalized proximal point method (GPPA) for
solving the nonlinear complementarity problem with monotone operators in
Rn. It differs from the classical proximal point method discussed
by Rockafellar for the problem of finding zeroes of monotone operators
in the use of generalized distances, called φ-divergences,
instead of the Euclidean one. These distances play not only a
regularization role but also a penalization one, forcing the sequence
generated by the method to remain in the interior of the feasible set,
so that the method behaves like an interior point one. Under appropriate
assumptions on the φ-divergence and the monotone operator we
prove that the sequence converges if and only if the problem has
solutions, in which case the limit is a solution. If the problem does
not have solutions, then the sequence is unbounded. We extend previous
results for the proximal point method concerning convex optimization
problems.

LA - eng

KW - Nonlinear complementarity problem; proximal point methods;
monotone operators.
; nonlinear complementarity problem; monotone operators

UR - http://eudml.org/doc/197803

ER -

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