A New Parameterization Algorithm for the Linear Complementarity Problem
We study a new parameterization algorithm for the P-matrix restriction of the linear complementarity problem. This parameterization can be considered similar to a path-following penalty method, and introduces to this class of algorithms a primal-dual symmetry similar to that seen in the highly successful path-following logarithmic barrier methods. The trajectory associated with the parameterization is distinguished by a naturally defined starting point and by a piecewise characterization as a fractional polynomial function of a single parameter. The trajectory can be followed exactly using root isolation and a simplex-like pivoting scheme. Convergence is guaranteed for a weakly-regular subclass of P-matrix LCPs. We show that under a weakly-regular and sign-invariant distribution for the input matrices and vectors, the average number of pieces in the trajectory is O(n 2), where n is the dimension of the problem space, and hence that the path-following algorithm has average-case polynomial running time.
KeywordsLinear complementarity path following probabilistic analysis sign-invariant.
Unable to display preview. Download preview PDF.
- M. Anitescu, G. Lesaja, and F. Potra (1995), “Equivalence between Various Formulations of the Linear Complementarity Problem,” Technical Report 71, Department of Mathematics, University of Iowa.Google Scholar
- G.E. Collins and R. Loos (1983), “Real Zeros of Polynomials,” in Computer Algebra, G.E. Collins and R. Loos, eds., Springer-Verlag, Wien, 84–94.Google Scholar
- K. Murty. (1983), Linear Programming, John Wiley and Sons.Google Scholar