On almost semimonotone matrices and the linear complementarity problem

In this paper, we revisit the class of almost (strictly) semimonotone matrices and partially address the conjecture made by Wendler [Spec. Matrices 7 (2019) 291-303]. We disprove the second part of the conjecture by providing a counter example. The main result of this paper shows that Wendler's conjecture is true under the symmetry assumption. We explore some interesting matrix theoretic properties of almost (strictly) semimonotone matrices and also present results pertaining to the existence and multiplicity of solutions to the linear complementarity problem associated with an almost semimonotone matrix. (c) 2022 Elsevier Inc. All rights reserved.