Search

The complementarity problem is defined and studied for cases where the constraints involve convex cones, thus extending the real and complex complementarity problems. Special cases of the problem are equivalent to dual, linear or quadratic, programs over polyhedral cones.

The basic solvability theorems of Farkas [2] and Levinson [4] were recently extended in different directions by Ben-Israel [1] and Kaul [3].The theorem stated in this note generalizes both results of Ben-Israel and Kaul and is applicable to nonlinear programming over complex cones.