A Newton method for a class of quasi-variational inequalities
This paper presents a variant of Newton's method to solve quasi- variational inequalities with monotonic operators. The problem considered can be described by the scheme: find \(y\) such that \[ \langle F(y), z- y\rangle\geq 0\qquad \text{for all} \quad z\in \Gamma(y), \] where (i) \(F\) is a continuously differentiable operator from \(A\subseteq \mathbb{R}^n\) to \(\mathbb{R}^n\). (ii) \(\Gamma(y)= \{z\in \mathbb{R}^n\): \(g_i(y, z)\leq 0,\;i= 1,2,\dots, s\}\) with \(g_i\) twice differentiable functions in the second variable. Some examples are considered.
scientific article; zbMATH DE number 754927
scientific article