Classes of functions and feasibility conditions in nonlinear complementarity problems

Given a mappingF from real Euclideann-space into itself, we investigate the connection between various known classes of functions and the nonlinear complementarity problem: Find anx* such thatFx* ⩾ 0 andx* ⩾ 0 are orthogonal. In particular, we study the extent to which the existence of au ⩾ 0 withFu ⩾ 0 (feasible point) implies the existence of a solution to the nonlinear complementarity problem, and extend, to nonlinear mappings, known results in the linear complementarity problem on P-matrices, diagonally dominant matrices with non-negative diagonal elements, matrices with off-diagonal non-positive entries, and positive semidefinite matrices.

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