Abstract
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.
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© 2000 Springer Science+Business Media Dordrecht
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Verma, S., Beling, P.A., Adler, I. (2000). A New Parameterization Algorithm for the Linear Complementarity Problem. In: Pardalos, P.M. (eds) Approximation and Complexity in Numerical Optimization. Nonconvex Optimization and Its Applications, vol 42. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3145-3_31
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DOI: https://doi.org/10.1007/978-1-4757-3145-3_31
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