On extremal behaviors of Murty's least index method
In this small note, we observe some extremal behaviors of Murty's least index method for solving linear complementarity problems. In particular, we show that the expected number of steps for solving Murty's exponential example with a random permutation of variable indices is exactly equal ton, wheren is the size of the input square matrix.
KeywordsLinear complementarity problems Murty's least index method Computational complexity
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- R.E. Cottle, J. Pang and R.E. Stone,The Linear Complementarity Problems (Academic Press, New York, 1992).Google Scholar
- K. Fukuda and T. Terlaky, “Linear complementarity and oriented matroids,”Journal of the Operations Research Society of Japan 35 (1992) 45–61.Google Scholar
- E. Klafszky and T. Terlaky, “Some generalizations of the criss-cross method for the linear complementarity problem of oriented matroids,”Combinatorica 9 (1989) 189–198.Google Scholar
- K. Murty, “Note on Bard-type scheme for solving the complementarity problem,”Opsearch 11 (1974) 123–130.Google Scholar
- K. Murty, “Computational complexity of complementary pivot methods,”Mathematical Programming Study 7 (1978) 61–73.Google Scholar
- J. Rohn, “A short proof of finiteness of Murty's principal pivoting algorithm,”Mathematical Programming, 46 (1990) 255–256.Google Scholar
- C. Roos, “An exponential example for Terlaky's pivoting rule for the criss-cross simplex method,”Mathematical Programming 46 (1990) 79–84.Google Scholar