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.


65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M15 Newton-type methods
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