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.


49J53 Set-valued and variational analysis
65K10 Numerical optimization and variational techniques
49M37 Numerical methods based on nonlinear programming
90C25 Convex programming
49J40 Variational inequalities