A new continuation method for complementarity problems with uniform P-functions
Mathematical Programming: Series A and B
Iterative descent algorithms for a row sufficient linear complementary problem
SIAM Journal on Matrix Analysis and Applications
On a Generalization of a Normal Map and Equation
SIAM Journal on Control and Optimization
Multiple-objective approximation of feasible but unsolvable linear complementarity problems
Journal of Optimization Theory and Applications
Global methods for nonlinear complementarity problems
Mathematics of Operations Research
Functions without exceptional family of elements and complementarity problems
Journal of Optimization Theory and Applications
Exceptional Families, Topological Degree and Complementarity Problems
Journal of Global Optimization
Solvability of implicit complementarity problems
Mathematical and Computer Modelling: An International Journal
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In this paper we establish several sufficient conditions for the existence of a solution to the linear and some classes of nonlinear complementarity problems. These conditions involve a notion of the ``exceptional family of elements'' introduced by Smith [19] and Isac, Bulavski and Kalashnikov [4], where the authors have shown that the nonexistence of the ``exceptional family of elements'' implies solvability of the complementarity problem. In particular, we establish several sufficient conditions for the nonexistence as well as for the existence of the exceptional family of elements.