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Classes of functions and feasibility conditions in nonlinear complementarity problems.(English)Zbl 0291.90059


MSC:

90C30 Nonlinear programming
90C25 Convex programming
65K05 Numerical mathematical programming methods

Cite

References:

[1]R. Chandrasekaran, ”A special case of the complementarity pivot problem”,Operations Research 7 (1970) 263–268.
[2]R.W. Cottle, ”Note on a fundamental theorem in quadratic programming”,SIAM Journal on Applied Mathematics 12 (1964) 663–665. ·Zbl 0128.39701 ·doi:10.1137/0112056
[3]R.W. Cottle, ”Nonlinear programs with positively bounded Jacobians”,SIAM Journal on Applied Mathematics 14 (1966) 147–157. ·Zbl 0158.18903 ·doi:10.1137/0114012
[4]R.W. Cottle and G.B. Dantzig, ”Positive (semi-) definite programming”, in:Nonlinear programming, Ed. J. Abadie (North-Holland, Amsterdam, 1967). ·Zbl 0178.22801
[5]C.W. Cryer, ”The solution of a quadratic programming problem using systematic overrelaxation”,SIAM Journal on Control 9 (1971) 385–392. ·Zbl 0216.54603 ·doi:10.1137/0309028
[6]C.W. Cryer, ”The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences”,Mathematics of Computation 25 (1971) 435–443. ·Zbl 0223.65044 ·doi:10.1090/S0025-5718-1971-0298961-7
[7]B.C. Eaves, ”The linear complementarity problem”,Management Science 17 (1971) 68–75. ·Zbl 0227.90044
[8]M. Edelstein, ”On fixed and periodic points under contractive mappings”,Journal of the London Mathematical Society 37 (1962) 74–79. ·Zbl 0113.16503 ·doi:10.1112/jlms/s1-37.1.74
[9]M. Fiedler and V. Pták, ”On matrices with non-positive off-diagonal elements and positive principal minors”,Czechoslovak Mathematical Journal 12 (1962) 382–400. ·Zbl 0131.24806
[10]C.B. Garcia, ”Some classes of matrices in linear complementarity theory”, Mathematical Programming 5 (1973) 299–310. ·Zbl 0284.90048 ·doi:10.1007/BF01580135
[11]A.W. Ingleton, ”A problem in linear inequalities”,Proceedings of the London Mathematical Society 16 (1966) 519–536. ·Zbl 0166.03005 ·doi:10.1112/plms/s3-16.1.519
[12]S. Karamardian, ”Existence of solutions of certain systems of nonlinear inequalities”,Numerische Mathematik 12 (1968) 327–334. ·Zbl 0167.48203 ·doi:10.1007/BF02162513
[13]C.E. Lemke, ”Recent results on complementarity problems”, in:Nonlinear programming, Eds. J.B. Rosen, O.L. Mangasarian and K. Ritter (Academic Press, New York, 1970). ·Zbl 0227.90043
[14]G.P. McCormick and R.A. Tapia, ”The gradient projection method under mild differentiability conditions”,SIAM Journal on Control 10 (1972) 93–98. ·Zbl 0237.49019 ·doi:10.1137/0310009
[15]G. Minty, ”Monotone (nonlinear) operators in Hilbert space”,Duke Mathematical Journal 29 (1962) 341–346. ·Zbl 0111.31202 ·doi:10.1215/S0012-7094-62-02933-2
[16]J.J. Moré, ”Nonlinear generalizations of matrix diagonal dominance with application to Gauss–Seidel iterations”,SIAM Journal on Numerical Analysis 9 (1972) 357–378. ·Zbl 0243.65023 ·doi:10.1137/0709035
[17]J.J. Moré, ”Coercivity conditions in nonlinear complementarity problems”,SIAM Review 16 (1974).
[18]J.J. Moré and W.C. Rheinboldt, ”On P- and S-functions and related classes ofn-dimensional nonlinear mappings”,Linear Algebra and Its Applications 6 (1973) 45–68. ·Zbl 0247.65038 ·doi:10.1016/0024-3795(73)90006-2
[19]W.C. Rheinboldt, ”On M-functions and their application to nonlinear Gauss–Seidel iterations, and network flows”,Journal of Mathematical Analysis and Applications 32 (1971) 274–307. ·Zbl 0206.46504 ·doi:10.1016/0022-247X(70)90298-2
[20]A. Tamir, ”The complementarity problem of mathematical programming”, Ph. D. thesis, Case Western Reserve University, Cleveland, Ohio (1973). ·Zbl 0277.15008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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