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Zbl 1178.49020
Moudafi, Abdellatif
From alternating minimization algorithms and systems of variational inequalities to equilibrium problems. (English)
[J] Commun. Appl. Nonlinear Anal. 16, No. 3, 31-35 (2009). ISSN 1074-133X

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 2000:: *49J53 Set-valued and variational analysis
65K10 Optimization techniques (numerical methods)
49M37 Methods of nonlinear programming type
90C25 Convex programming
49J40 Variational methods including variational inequalities

Keywords: variational inequalities; alternating minimization algorithms; projection methods; equilibrium problems

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Zentralblatt MATH Berlin [Germany]