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A cutting plane algorithm for solving bilinear programs.(English)Zbl 0353.90069


MSC:

90C20 Quadratic programming

Cite

References:

[1]M. Altman, ”Bilinear programming”,Bullentin de l’Académie Polonaise des Sciences 16 (9) (1968) 741–746. ·Zbl 0213.44902
[2]E. Balas and C.-A. Burdet, ”Maximizing a convex quadratic function subject to linear constraints”, Management Science Research Report No. 299, GSIA, Carnegie-Mellon University, Pittsburgh, Pa. (July 1973).
[3]A.V. Cabot and R.L. Francis, ”Solving certain nonconvex quadratic minimization problems by ranking extreme points”,Operations Research 18 (1) (1970) 82–86. ·Zbl 0186.24201 ·doi:10.1287/opre.18.1.82
[4]A. Charnes and W.W. Cooper, ”Nonlinear power of adjacent extreme point methods in linear programming”,Econometrica 25 (1957) 132–153. ·Zbl 0087.16404 ·doi:10.2307/1907747
[5]W. Candler and R.J. Townsley, ”The Maximization of a quadratic function of variables subject to linear inequalities”,Management Science 10 (3) (1964) 515–523. ·doi:10.1287/mnsc.10.3.515
[6]R.W. Cottle and W.C. Mylander, ”Ritter’s cutting plane method for nonconvex quadratic programming”, in: J. Abadie, ed.,Integer and nonlinear programming (North Holland, Amsterdam, 1970). ·Zbl 0332.90033
[7]G.B. Dantzig, ”Reduction of a 0–1 integer program to a bilinear separable program and to a standard complementary problem”, Unpublished Note, July 27, 1971.
[8]G.B. Dantzig, ”Solving two-move games with perfect information”, RAND Report P-1459, Santa Monica, Calif. (1958).
[9]J. Falk, ”A linear max-min problem”, Mathematical Programming 5 (1973) 169–188. ·Zbl 0276.90053 ·doi:10.1007/BF01580119
[10]G. Gallo and A. Ülkücü, ”Bilinear programming: an exact algorithm”, Paper presented at the 8th International Symposium on Mathematical Programming, Stanford University, Stanford, California, August 1973.
[11]K. Konno, ”Maximization of convex quadratic function under linear constraints”,Mathematical Programming 11 (1976) to appear. ·Zbl 0355.90052
[12]H. Konno, ”Bilinear programming part II: applications of bilinear programming”, Tech. Rept. No. 71-10, Department of Operations Research, Stanford University, Stanford, Calif. (August 1971).
[13]O.L. Mangasarian, ”Equilibrium points of bimatrix games”,SIAM Journal of Applied Mathematics 12 (4) (1964) 778–780. ·Zbl 0132.14002 ·doi:10.1137/0112064
[14]O.L. Mangasarian and H. Stone, ”Two-person nonzero-sum games and quadratic programming”,Journal of Mathematical Analysis and Applications 9 (1964) 348–355. ·Zbl 0126.36505 ·doi:10.1016/0022-247X(64)90021-6
[15]H. Mills, ”Equilibrium points in finite games”,SIAM Journal of Applied Mathematics 8 (2) (1960) 397–402. ·Zbl 0099.15201 ·doi:10.1137/0108026
[16]W.C. Mylander, ”Nonconvex quadratic programming by a modification of Lemke’s method”, RAC-TP-414, Research Analysis Corporation, McLean, Va. (1971).
[17]K. Ritter, ”A method for solving maximum problems with a nonconcave quadratic objective function”,Zeitung für Wahrscheinlichkeitstheorie und verwandte Gebiete 4 (1966) 340–351. ·Zbl 0139.13105 ·doi:10.1007/BF00539118
[18]M. Raghavachari, ”On connections between zero-one integer programming and concave programming under linear constraints”,Operations Research 17 (4) (1969) 680–684. ·Zbl 0176.49805 ·doi:10.1287/opre.17.4.680
[19]H. Tui, ”Concave programming under linear constraints”,Soviet Mathematics (1964) 1537–1440. ·Zbl 0132.40103
[20]P. Zwart, ”Nonlinear programming: counterexamples to two global optimization algorithms”,Operations Research 21 (6) (1973) 1260–1266. ·Zbl 0274.90049 ·doi:10.1287/opre.21.6.1260
[21]P. Zwart, ”Computational aspects of the use of cutting planes in global optimization”, in:Proceedings of the 1971 annual conference of the ACM (1971) pp. 457–465.
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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