• Corpus ID: 275568801

Pivoting in Linear Complementarity Two Polynomial-Time Cases

@inproceedings{FoniokPivotingIL,
  title={Pivoting in Linear Complementarity Two Polynomial-Time Cases},
  author={Jan Foniok and Komei Fukuda and Bernd G{\"a}rtner and Hans-Jakob L{\"u}thi and Hans-Jakob L{\"u}thi},
  url={https://api.semanticscholar.org/CorpusID:275568801}
}
We study the behavior of simple principal pivoting methods for the P-matrix linear complementarity problem (P-LCP). We solve an open problem of Morris by showing that Murty’s least-index pivot rule (under any fixed index order) leads to a quadratic number of iterations on Morris’s highly cyclic P-LCP examples. We then show that on K-matrix LCP instances, all pivot rules require only a linear number of iterations. As the main tool, we employ unique-sink orientations of cubes, a useful… 
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30 References

Randomized pivot algorithms for P-matrix linear complementarity problems

It is shown that orientations of the n-cube that come from simple principal pivot algorithms for the linear complementarity problem with a P-matrix properly generalize those that are obtained from linear objective functions on polytopes combinatorially equivalent to the cube.

Digraph Models of Bard-Type Algorithms for the Linear Complementarity Problem

These digraphs show that such algorithms based on complementary pivoting for solving the linear complementarity problem can cycle even for symmetric, positive deFinite M, and provide some insight into the algorithms' behavior.

Unique Sink Orientations of Grids

It is shown that the orientations arising from PGLCP satisfy the Holt-Klee condition known to hold for polytope digraphs, and the first expected linear-time algorithms for solvingPGLCP with a fixed number of blocks are given.

LINEAR COMPLEMENTARITY AND ORIENTED MATROIDS

A combinatorial abstraction of the linear complementarity theory in the setting of oriented matroids was first considered by M.J. Todd. In this paper, we take a fresh look at this abstraction, and…

Fast Solutions of Complementarity Formulations in American Put Pricing

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NP-Completeness of the linear complementarity problem

We consider the linear complementarity problem (q, M) for which the data are the integer column vectorq εRn and the integer square matrixM of ordern. GLCP is the decision problem: Does (q, M) have a…

Computational complexity of complementary pivot methods

The class of orthants in R n contains 2n orthants. A straight line L in R n is said to cut across an orthant C of R n if L has a nonempty intersection with the interior of C. It is well known that…

Pricing American Put Options by Fast Solutions of the Linear Complementarity Problem

It is shown in a constructive fashion that a new algorithm may be devised which processes the original LCP in linear number of spatial grid points.

HOW GOOD IS THE SIMPLEX ALGORITHM

By constructing long 'increasing' paths on appropriate convex polytopes, it is shown that the simplex algorithm for linear programs is not a 'good algorithm' in the sense of J. Edmonds.

EP Theorems and Linear Complementarity Problems