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From alternating minimization algorithms and systems of variational inequalities to equilibrium problems. (English) Zbl 1178.49020
Summary: Using equilibrium problems, we establish a link between alternating minimization algorithms, composition of resolvent of monotone operators and systems of variational inequalities. This approach allows us not only to generalize several known results in nonlinear analysis and their presentation in a unified way, but also to yield new insights into variational inequality systems close to those introduced by Verma.

MSC:
49J53Set-valued and variational analysis
65K10Optimization techniques (numerical methods)
49M37Methods of nonlinear programming type in calculus of variations
90C25Convex programming
49J40Variational methods including variational inequalities