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On the gradient-projection method for solving the nonsymmetric linear complementarity problem. (English) Zbl 0517.90083


MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[2] Lemke, C. E.,Bimatrix Equilibrium Points and Mathematical Programming, Management Science, Vol. 11, pp. 681-689, 1965. · Zbl 0139.13103 · doi:10.1287/mnsc.11.7.681
[3] Murty, K. G.,Computational Complexity of Complementary Pivot Method, Mathematical Programming Study, Vol. 7, pp. 61-73, 1978. · Zbl 0381.90108
[4] Bertsekas, D. P.,On the Goldstein-Levitin-Poljak Gradient-Projection Method, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 174-184, 1976. · Zbl 0326.49025 · doi:10.1109/TAC.1976.1101194
[5] Levitin, E. S., andPoljak, B. T.,Constrained Minimization Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 6, pp. 1-50, 1966. · doi:10.1016/0041-5553(66)90114-5
[6] Fielder, M., andPtak, V.,On Matrices with Nonpositive Off-Diagonal Elements and Positive Principal Minors, Czechoslovak Mathematics Journal, Vol. 12, pp. 382-400, 1962.
[7] Murty, K. G.,On the Number of Solutions to the Complementarity Problem and Spanning Properties of Complementarity Cones, Linear Algebra and Applications, Vol. 5, pp. 65-108, 1972. · Zbl 0241.90046 · doi:10.1016/0024-3795(72)90019-5
[8] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
[9] Cheng, Y. C.,Iterative Methods for Solving Linear Complementarity and Linear Programming Problems, University of Wisconsin, Madison, Wisconsin, PhD Thesis, 1981.
[10] Ortega, J. M.,Numerical Analysis: A Second Course, Academic Press, New York, New York, 1972. · Zbl 0248.65001
[11] Poljak, B. T.,On a Sharp Minimum, University of Wisconsin, Mathematics Research Center, Seminar, 1980. · Zbl 0472.90049
[12] Mangasarian, O. L., andMeyer, R. R.,Nonlinear Perturbation of Linear Programs, SIAM Journal of Control and Optimization, Vol. 17, pp. 745-752, 1979. · Zbl 0432.90047 · doi:10.1137/0317052
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