Integral global optimization method for solution of nonlinear complementarity problems (Q1337131)

One considers the nonlinear complementary problem: find \(x\in \mathbb{R}^n\) such that \(x\in {\mathcal O}\), \(f(x)\in {\mathcal O}^*\), \(\langle x, f(x)\rangle= 0\), where \(\mathcal O\) is an orthant in \(\mathbb{R}^n\). The main hypothesis on the function \(f\) is that it is robust piecewise continuous (i.e. there is a partition \((V_\lambda)\) of \(\mathbb{R}^n\) composed by robust sets such that \(f|_{V_\lambda}\) is continuous for every \(\lambda\)) and is a nondegenerate \(P\)-mapping. Under some additional assumptions it is shown that the NCP problem is solvable by an integral optimization method.