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2004 | 2 | 1 | 76-86
Tytuł artykułu

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

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Strony
76-86
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
Twórcy
autor
Bibliografia
  • [1] C.E. Lemke, J.T. Howson: “Equilibrium points of bimatrix games”, SIAM Review., Vol. 12, (1964), pp. 45–78.
  • [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
  • [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.
  • [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
  • [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
  • [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
  • [12] L.D. Popov: “On the approximative roots of maximal monotone mapping”, Yugoslav Journal of Operations Research, Vol. 6, (1996), pp. 19–32.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475952
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