Abstract
A power penalty approach has been proposed to linear complementarity problem but not to Horizontal Linear Complementarity Problem (HLCP) because the coefficient matrix is not positive definite. It is skillfully proved that HLCP is equivalent to a variational inequality problem and a mixed linear complementarity problem for the first time. A power penalty approach is proposed to the mixed linear complementarity problem based on approximating the HLP by a nonlinear equation. It has been proved that the solution to this equation is feasible and converges to that of the HLP at a rate of at least O(&lambda)<sup>-k/2</sup> in the Euclidean norm.
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