A class of nonlinear complementarity problems for multifunctions. (English) Zbl 0593.90078

Parida, J.; Sen, A.

J. Optimization Theory Appl. 53, 105-113 (1987).

Summary: Given a continuous map \(F: R^ n\to R^ n\) and a lower semicontinuous positively homogeneous convex function \(h: R^ n\to R\), the nonlinear complementarity problem considered here is to find \(x\in R^ n_+\) and yC\(\partial h(x)\), the subdifferential of h at x, such that \(F(x)+y\geq 0\) and \(x^ T(F(x)+y)=0\). Some existence theorems for the above problem are given under certain conditions on the map F. An application to quasidifferentiable convex programming is also shown.

MSC:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C25	Convex programming

Keywords:

lower semicontinuous positively homogeneous convex function; nonlinear complementarity; subdifferential; quasidifferentiable convex programming; multifunctions

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