On the Equivalence of the Linear Complementarity Problem and a System of Piecewise Linear Equations: Part II
In an earlier paper the authors demonstrated the equivalence of the linear complementarity problem and that of finding the zeroes of a square system of equations for which the functions are piecewise linear. Given the system of equations, a “dual” concept of complementarity was evoked to pose the problem as an LCP.
In this paper, with the simplifying assumption of a non-degenerate finite sub-division defined by hyperplanes, a simplified equivalence is demonstrated, wherein “complementarity” refers only to the positive vs negative sides of a hyperplane.
Key wordsPiecewise linear linear complementarity subdivision by hyperplanes Non-degenerate
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