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

MSC:
90C20 Quadratic programming
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[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
[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
[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.
[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Dantzig, ”Reduction of a 0–1 integer program to a bilinear separable program and to a standard complementary problem”, Unpublished Note, July 27, 1971.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
[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
[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
[15] H. Mills, ”Equilibrium points in finite games”,SIAM Journal of Applied Mathematics 8 (2) (1960) 397–402. · Zbl 0099.15201
[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
[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
[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
[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.
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