A cutting plane algorithm for solving bilinear programs

Hiroshi Konno

doi:10.1007/bf01580367

journal article Dec 01, 1976

A cutting plane algorithm for solving bilinear programs

Hiroshi Konno

Mathematical Programming Vol. 11 No. 1 pp. 14-27 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01580367

Topics

No keywords indexed for this article. Browse by subject →

References

21

[1]

M. Altman, “Bilinear programming”,Bullentin de l'Académie Polonaise des Sciences 16 (9) (1968) 741–746.

[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. 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. 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. 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).

[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Dantzig, “Reduction of a 0–1 integer program to a bilinear separable program and to a standard complementary problem”, Unpublished Note, July 27, 1971.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. 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. 10.1007/bf01580380

[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. 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. 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. 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. 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. 10.1287/opre.17.4.680

[19]

H. Tui, “Concave programming under linear constraints”,Soviet Mathematics (1964) 1537–1440.

[20]

P. Zwart, “Nonlinear programming: counterexamples to two global optimization algorithms”,Operations Research 21 (6) (1973) 1260–1266. 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. 10.1145/800184.810515

Cited By

195

Robust Scheduling of Integrated Electricity and Heating System Hedging Heating Network Uncertainties

Zhou Huansheng, Zhigang Li · 2020

IEEE Transactions on Smart Grid

Metrics

195

Citations

21

References

Details

Published: Dec 01, 1976
Vol/Issue: 11(1)
Pages: 14-27
License: View

Authors

H

Hiroshi Konno

Cite This Article

Hiroshi Konno (1976). A cutting plane algorithm for solving bilinear programs. Mathematical Programming, 11(1), 14-27. https://doi.org/10.1007/bf01580367

A cutting plane algorithm for solving bilinear programs

You May Also Like