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Alber, Ya. I.

The penalty method for variational inequalities with nonsmooth unbounded operators in Banach space. (English) Zbl 0867.49009

Numer. Funct. Anal. Optimization 16, No. 9-10, 1111-1125 (1995).
Summary: We study the existence of a solution and convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in a Banach space. All the objects of the inequality – the operator, “the data” and the set of constraints – are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the space and its dual. The results of this paper extend and generalize results of J. L. Lions [“Quelques méthodes de résolution des problèmes aux limites non linéaires” (1969; Zbl 0189.40603)]. They are new even in Hilbert spaces.

Cited in 1 Review
Cited in 5 Documents

MSC:

49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49M30 Other numerical methods in calculus of variations (MSC2010)

Keywords:

penalty method; variational inequalities; monotone operators in a Banach space; stability theorems; Hilbert spaces

Citations:

Zbl 0189.40603
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\textit{Ya. I. Alber}, Numer. Funct. Anal. Optim. 16, No. 9--10, 1111--1125 (1995; Zbl 0867.49009)
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References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.