Two new self-adaptive projection methods for variational inequality problems. (English) Zbl 1012.65064
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.
Reviewer: Viorel Arnautu (Iasi)
MSC:
| 65K10 | Numerical optimization and variational techniques |
| 49J40 | Variational inequalities |
| 49M15 | Newton-type methods |
Keywords:
self-adaptive projection methods; numerical examples; variational inequality; line search strategyReferences:
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