無

In this paper, we establish existence theory and algorithms on
variational problems, by which we mean here problems of fixed
points, coincidences, minimax inequalities, generalized variat-
ional inequalities, generalized quasi-variational inequalities.
Under weakened assumptions on the operators and constraint reg-
ions, we improve and generalize recently many well-known exist-
ence theorems. More specifically, we establish two versions of
Nikaidos coincidence theorem from different approaches, and use
these to show several existence theorems for the generalized v-ariational inequalities, in the case that C is noncompact and
nonconvex, but merely a nearly convex set. Also, we introduce
a new Bregman-type proximal point algorithm for solving variat-
ional inequalitiy problems in a reflexive Banach space, and pr-
ovide a continuation method to solve nonsmooth convex programm-
ing.

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