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**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 strategy
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\textit{D. Han} and \textit{H. K. Lo}, Comput. Math. Appl. 43, No. 12, 1529--1537 (2002; Zbl 1012.65064)

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