A New Parameterization Algorithm for the Linear Complementarity Problem

  • Sushil Verma
  • Peter A. Beling
  • Ilan Adler
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 42)


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.


Linear complementarity path following probabilistic analysis sign-invariant. 


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Sushil Verma
    • 1
  • Peter A. Beling
    • 2
  • Ilan Adler
    • 3
  1. 1.i2 TechnologiesRedwood CityUSA
  2. 2.Department of Systems EngineeringUniversity of VirginiaCharlottesvilleUSA
  3. 3.Department of Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeleyUSA

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