The existence of solutions for set-valued nonlinear complementarity problems. (Chinese. English summary) Zbl 1174.90849
Summary: The set-valued nonlinear complementarity problems are studied. First, a new auxiliary function is constructed to transform the set-valued nonlinear complementarity problems into fixed point problems. By utilizing the Leary-Schauder fixed point theorem, a sufficient condition is given for the existence of the solution to the set-valued nonlinear complementarity problems. The results generalize some well-known existence theorems. Then, Leary-Schauder fixed point algorithm is established to solve the nonlinear complementarity problems.
MSC:
90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
54C60 | Set-valued maps in general topology |