# On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

Open Mathematics (2004)

- Volume: 2, Issue: 1, page 76-86
- ISSN: 2391-5455

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topL. Popov. "On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method." Open Mathematics 2.1 (2004): 76-86. <http://eudml.org/doc/268770>.

@article{L2004,

abstract = {For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.},

author = {L. Popov},

journal = {Open Mathematics},

keywords = {65K05; 90C20; 90C49},

language = {eng},

number = {1},

pages = {76-86},

title = {On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method},

url = {http://eudml.org/doc/268770},

volume = {2},

year = {2004},

}

TY - JOUR

AU - L. Popov

TI - On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

JO - Open Mathematics

PY - 2004

VL - 2

IS - 1

SP - 76

EP - 86

AB - For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.

LA - eng

KW - 65K05; 90C20; 90C49

UR - http://eudml.org/doc/268770

ER -

## References

top- [1] C.E. Lemke, J.T. Howson: “Equilibrium points of bimatrix games”, SIAM Review., Vol. 12, (1964), pp. 45–78. Zbl0128.14804
- [2] R.W. Cottle, G.B. Dantzig: “Complementarity pivote theory of mathematical programming”, Linear Algebra and its Applications, Vol. 1, (1968), pp. 103–125. http://dx.doi.org/10.1016/0024-3795(68)90052-9
- [3] B.C. Eaves: “The linear complementarity problem”, Management Science., Vol. 17, (1971), pp. 612–634. http://dx.doi.org/10.1287/mnsc.17.9.612 Zbl0228.15004
- [4] M. Aganagic, R.W. Cottle: “A constructive characterization of Q 0-matrices with nonnegative principal minors”, Math. Programming., Vol. 37, (1987), pp. 223–231. Zbl0618.90091
- [5] R.W. Cottle, J.S. Pang, R.E. Stone: The Linear Complementarity Problem, Academic Press, Boston, 1992.
- [6] O.L. Managasarian: “The ill-posed linear complementarity problem”, In: M.C. Ferris, J.S. Pang: Complementarity and variational problems: State of the Art, SIAM Publications, Philadelphia, PA, 1997, pp. 226–233.
- [7] I.I. Eremin: Theory of Linear Optimization, Inverse and Ill-Posed Problems Series. VSP. Utrecht, Boston, Koln, Tokyo, 2002.
- [8] I.I. Eremin, Vl.D. Mazurov, N.N. Astaf’ev: Improper Problems of Linear and Convex Programming, Nauka, Moscow. 1983. (in Russian)
- [9] Y. Fan, S. Sarkar, and L. Lasdon: “Experiments with successive quadratic programming algorithms”, J. Optim. Theory Appl., VOl. 56, (1988), pp. 359–383. http://dx.doi.org/10.1007/BF00939549 Zbl0619.90056
- [10] P.E. Gill, W. Murray, A.M. Saunders: “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization”, SIAM Journal on Optimization, Vol. 12, (2002), pp. 979–1006. http://dx.doi.org/10.1137/S1052623499350013 Zbl1027.90111
- [11] G. Isac, M.M. Kostreva, M.M. Wiecek: “Multiple objective approximation of feasible but unsolvable linear complementarity problems”, Journal of Optimization Theory and Applications, Vol. 86, (1995), pp. 389–405. http://dx.doi.org/10.1007/BF02192086 Zbl0838.90120
- [12] L.D. Popov: “On the approximative roots of maximal monotone mapping”, Yugoslav Journal of Operations Research, Vol. 6, (1996), pp. 19–32. Zbl0851.65043

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