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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.

65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
49M15Newton-type methods in calculus of variations
Full Text: DOI
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