In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish importance $E_0^s$-matrices in context complementarity theory. show that principal pivot transform $E_0^s$-matrix is not necessarily $E_0^s$ general. However, prove $\tilde{E_0^s}$-matrices, a subclass with some additional conditions, $E_0^f$ by showing $P_0.$ LCP$(q, A)$ can be processable Lemke's alg...

We revisit the class of column competent matrices and study some matrix theoretic properties this class. The local w-uniqueness solutions to linear complementarity problem can be identified by matrices. establish new results on in connection with These are significant context theory as well algorithms operations research. prove locally property Finally, we a between adequate help degree theory.

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Recently Tseng (Math Program 83:159–185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204–225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related pro...