2 research outputs found
A generalized proximal point algorithm for the nonlinear complementarity problem
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