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Zbl 1012.65064
Han, Deren; Lo, Hong K.
Two new self-adaptive projection methods for variational inequality problems.
(English)
[J] Comput. Math. Appl. 43, No.12, 1529-1537 (2002). ISSN 0898-1221

The usual variational inequality Find $u^* \in K$ such that $$F(u^*)^T (v-u^*) \geq 0 \quad\text{for any }v \in K,$$ where $K$ is a nonempty closed convex subset of $R^n$, is considered. The function $F$ is continuous and satisfies only some generalized monotonicity assumptions. The new methods use only function evaluations and projections onto the set $K$, together with a line search strategy. Numerical tests are reported.
[Viorel Arnautu (Iasi)]
MSC 2000:
*65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

Keywords: self-adaptive projection methods; numerical examples; variational inequality; line search strategy

Cited in: Zbl 1200.65053

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