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Iteration penalty method in Hilbert spaces

Let if be a closed convex subset of V. An element f gV and an operator A U — U are given. We assume that A is a bounded semicontinuous and strongly monotonous operator, i.e. [Pg.43]

In the sequel, the following variational inequality is analysed to find u G K such that [Pg.44]

Let us construct the standard penalty operator (5 v) = I v — Pv) and define the penalty problem depending on a small positive parameter s, [Pg.44]

Repeating the proof of Theorem 1.19 for this case, one deduces that equation (1.119) has a unique solution gV which satisfies [Pg.44]

To linearize the penalty operator in (1.119) we use the following iteration scheme similar to (1.105), [Pg.44]


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