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Solution of symmetric linear complementarity problems by iterative methods. (English) Zbl 0341.65049

65K05Mathematical programming (numerical methods)
90C05Linear programming
Full Text: DOI
[1] Lemke, C. E.,On Complementary Pivot Theory, Mathematics of the Decision Sciences, Part 1, Edited by G. B. Dantzig and A. F. Veinott, American Mathematical Society, Providence, Rhode Island, pp. 95-114, 1968. · Zbl 0208.45502
[2] Cottle, R. W., andDantzig, G. B.,Complementary Pivot Theory of Mathematical Programming, Linear Algebra and Its Applications, Vol. 1, pp. 103-125, 1968. · Zbl 0155.28403 · doi:10.1016/0024-3795(68)90052-9
[3] Murty, K. G.,On the Number of Solutions to the Complementarity Problem and Spanning Properties of Complementary Cones, Linear Algebra and Its Applications, Vol. 5, pp. 65-108, 1972. · Zbl 0241.90046 · doi:10.1016/0024-3795(72)90019-5
[4] Mangasarian, O. L.,Linear Complementarity Problems Solvable by a Single Linear Program, Mathematical Programming, Vol. 10, pp. 263-270, 1976. · Zbl 0355.90040 · doi:10.1007/BF01580671
[5] Mangasarian, O. L.,Solution of Linear Complementary Problems by Linear Programming, Numerical Analysis Dundee 1975, Edited by G. W. Watson, Springer-Verlag, Berlin, Germany, pp. 166-175, 1976.
[6] Mangasarian, O. L.,Characterization of Linear Complementarity Problems as Linear Programs, University of Wisconsin, Madison, Wisconsin, Computer Sciences Report No. 271, 1976. · Zbl 0349.90068
[7] Cryer, C. W.,The Method of Christopherson for Solving Free Boundary Problems for Infinite Journal Bearings by Means of Finite Differences, Mathematics of Computation, Vol. 25, pp. 435-443, 1971. · Zbl 0223.65044 · doi:10.1090/S0025-5718-1971-0298961-7
[8] Eckhardt, U.,Quadratic Programming by Successive Overrelaxation, Kernforschungsanlage Jülich, Technical Report No. Jül-1064-MA, 1974.
[9] Raimondi, A. A., andBoyd, J.,A Solution for the Finite Journal Bearing and Its Application to Analysis and Design, III, Transactions of the American Society of Lubrication Engineers, Vol. 1, pp. 194-209, 1958.
[10] Fridman, V. M., andChernina, V. S.,An Iteration Process for the Solution of the Finite-Dimensional Contact Problem, USSR Computational Mathematics and Mathematical Physics, Vol. 8, pp. 210-214, 1967. · doi:10.1016/0041-5553(67)90071-7
[11] Ortega, J. M.,Numerical Analysis, A Second Course, Academic Press, New York, New York, 1972. · Zbl 0248.65001
[12] Gnanadoss, A. A., andOsborne, M. R.,The Numerical Solution of Reynolds’ Equation for a Journal Bearing, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 17, pp. 241-246, 1964. · Zbl 0244.65077 · doi:10.1093/qjmam/17.2.241
[13] Martinet, B.,Convergence de Certaines Méthodes de Relaxation en Programmation Convexe, Comptes Rendus de L’Académie des Sciences, Paris, France, Vol. 265, Series A, pp. 210-212, 1967. · Zbl 0153.21302
[14] Cryer, C. W.,The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation, SIAM Journal on Control, Vol. 9, pp. 385-392, 1971. · Zbl 0216.54603 · doi:10.1137/0309028
[15] Glowinski, R.,Sur la Minimisation, par Surrelaxation avec Projection, de Functionnelles, Quadratiques dans les Espaces d’Hilbert, Comptes Rendus de L’Académie des Sciences, Paris, France, Vol. 276, Series A, pp. 1421-1423, 1973. · Zbl 0255.49023
[16] Martinet, B., andAuslender, A.,Methodes de Decomposition pour la Minimisation d’une Fonction sur une Espace Produit, SIAM Journal on Control, Vol. 12, pp. 635-642, 1974. · Zbl 0302.49025 · doi:10.1137/0312047
[17] Cottle, R. W., Golub, G. H., andSacher, R. S.,On the Solution of Large Structured Linear Complementarity Problems, III, Stanford University, Stanford, California, Operations Research Report No. 73-8, 1973.
[18] Young, D. M.,Iterative Solution of Large Linear Systems, Academic Press, New York, New York, 1971. · Zbl 0231.65034
[19] Fiedler, M., andPták, V.,On Matrices with Non-Positive Off-Diagnonal Elements and Positive Principal Minors, Czechoslovak Mathematics Journal, Vol. 12, pp. 382-400, 1962. · Zbl 0131.24806
[20] Varga, R. S.,Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962.
[21] Varga, R. C.,On Recurring Theorems on Diagonal Dominance, Linear Algebra and Its Applications, Vol. 13, pp. 1-9, 1976. · Zbl 0336.15007 · doi:10.1016/0024-3795(76)90037-9
[22] Levitin, E. S., andPoljak, B. T.,Constrained Minimization Methods, USSR Computational Mathematics and Mathematical Physics, Vol. 6, pp. 1-50, 1966. · doi:10.1016/0041-5553(66)90114-5
[23] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
[24] Ostrowski, A. M.,Solution of Equations and Systems of Equations, Second Edition, Academic Press, New York, New York, 1966. · Zbl 0222.65070
[25] Daniel, J. W.,The Approximate Minimization of Functionals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. · Zbl 0223.65014