Algebraically Equivalent Transformation Technique for Weighted Linear Complementarity Problems

Abstract

Abstract We study the algebraically equivalent transformation technique using an application implemented in the Java programming language that solves weighted linear complementarity problems. In general, in the case of the algebraically equivalent transformation, we divide the nonlinear equation of the system that characterizes the central path, the so-called centrality equation, by the barrier parameter. However, in this case, we divide, component-wise, the centrality equation by the right-hand side vector, which depends on the barrier parameter. We apply the same continuously differentiable and invertible function to both sides of the obtained equation and generate different search directions using Newton’s method. We analyze the numerical results provided by our application in the case of applying the algebraically equivalent transformation technique using the identical map and the square root function.