DOI: 10.1007/bf01581626. A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts

A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts

10.1007/bf01581626

Crossref journal-article

Springer Science and Business Media LLC

Mathematical Programming (297)

Bibliography

Sherali, H. D., & Shetty, C. M. (1980). A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts. Mathematical Programming, 19(1), 14â31.

Authors 2

Hanif D. Sherali (first)
C. M. Shetty (additional)

References 26 Referenced 64

M. Altman, “Bilinear programming”,Bulletin d'Academie Polonaise des Sciences 16(9) (1968) 741–746. / Bulletin d'Academie Polonaise des Sciences by M. Altman (1968)
E. Balas, “Intersection cuts—A new type of cutting planes for integer programming”,Operations Research 19 (1971) 19–39. (10.1287/opre.19.1.19) / Operations Research by E. Balas (1971)
E. Balas, “Intersection cuts from disjunctive constraints”, Management Science Research Report No. 330, Carnegie-Mellon University (Pittsburg, PA, February 1974). / “Intersection cuts from disjunctive constraints”, Management Science Research Report No. 330 by E. Balas (1974)
E. Balas and C.A. Burdet, “Maximizing a convex quadratic function subject to linear constraints”, Management Science Research Report No. 299, Carnegie-Mellon University (Pittsburg, PA, July 1973). / “Maximizing a convex quadratic function subject to linear constraints”, Management Science Research Report No. 299 by E. Balas (1973)
C.A. Burdet, “Polaroids: A new tool in nonconvex and in integer programming”,Naval Research Logistics Quarterly 20 (1973) 13–22. (10.1002/nav.3800200103) / Naval Research Logistics Quarterly by C.A. Burdet (1973)
C.A. Burdet, “On polaroid intersections”, in: P. Hammer and G. Zoutendijk, eds.,Mathematical programming in theory and practice (North-Holland, Amsterdam, 1974). / Mathematical programming in theory and practice by C.A. Burdet (1974)
F. Glover, “Polyhedral convexity cuts and negative edge extensions”,Zeitschrift für Operations Research 18 (1974) 181–186. / Zeitschrift für Operations Research by F. Glover (1974)
F. Glover, “Polyhedral annexation in mixed integer and combinatorial programming”,Mathematical Programming 8 (1975) 161–188. (10.1007/BF01681342) / Mathematical Programming by F. Glover (1975)
B. Grünbaum,Convex polytopes (Interscience, New York, 1967). / Convex polytopes by B. Grünbaum (1967)
R.G. Jeroslow, “The principles of cutting plane theory: Part I” (with an addendum), GSIA, Carnegie-Mellon University (Pittsburg, PA, February 1974). / “The principles of cutting plane theory: Part I” (with an addendum) by R.G. Jeroslow (1974)
R.G. Jeroslow, “Cutting-plane theory: Disjunctive methods”,Annals of Discrete Mathematics 1 (1977) 293–330. (10.1016/S0167-5060(08)70741-6) / Annals of Discrete Mathematics by R.G. Jeroslow (1977)
H. Konno, “Bilinear programming, Parts I and II”, Technical Report No. 71-9 and 71-10, Dept. of Operations Research, Stanford University (Stanford, CA, 1971). / “Bilinear programming, Parts I and II”, Technical Report No. 71-9 and 71-10 by H. Konno (1971)
H. Konno, “A cutting plane algorithm for solving bilinear programs”,Mathematical Programming 11 (1976) 14–27. (10.1007/BF01580367) / Mathematical Programming by H. Konno (1976)
H. Konno, “Maximization of a convex quadratic function under linear constraints”,Mathematical Programming 11 (1976) 117–127. (10.1007/BF01580380) / Mathematical Programming by H. Konno (1976)
A. Majthey and A. Whinston, “Quasi-concave minimization subject to linear constraints”,Discrete Mathematics 9 (1974) 35–59. (10.1016/0012-365X(74)90070-3) / Discrete Mathematics by A. Majthey (1974)
G. Owen, “Cutting planes for programs with disjunctive constraints”,Optimization Theory and its Applications 11 (1973) 29–55. / Optimization Theory and its Applications by G. Owen (1973)
H.D. Sherali and C.M. Shetty, “Deep cuts in disjunctive programming”, Paper presented at the Joint National ORSA/TIMS Meeting, New Orleans, LA (May 1979).
C.M. Shetty and S. Selim, “Stochastic location—allocation problems and bi-convex programming”, Presented at the ORSA/TIMS Meeting, New York, (May 1978).
C.M. Shetty and H.D. Sherali, “Rectilinear distance location—allocation problem: A simplex based algorithm”,Proc. of the Internat. Symp. on Extremal Methods and Systems Analysis, Lecture Notes in Economics and Math. Systems (Springer, 1980). (10.1007/978-3-642-46414-0_23)
R.M. Soland, “Optimal facility location with concave costs”,Operations Research 22 (1974) 373–382. (10.1287/opre.22.2.373) / Operations Research by R.M. Soland (1974)
H. Vaish, “Nonconvex programming with applications to production and location problems”, Unpublished Ph.D. Dissertation, Georgia Institute of Technology (Atlanta, GA, 1974). / Nonconvex programming with applications to production and location problems by H. Vaish (1974)
H. Vaish and C.M. Shetty, “A cutting plane algorithm for the bilinear programming problem”,Naval Research Logistics Quarterly 24 (1977) 83–94. (10.1002/nav.3800240107) / Naval Research Logistics Quarterly by H. Vaish (1977)
H. Vaish and C.M. Shetty, “The bilinear programming problem”,Naval Research Logistics Quarterly 23 (1976) 303–309. (10.1002/nav.3800230212) / Naval Research Logistics Quarterly by H. Vaish (1976)
P. Zwart, “Nonlinear programming: counter examples to two global optimization algorithms”,Operations Research 21 (1973) 1260–1266. (10.1287/opre.21.6.1260) / Operations Research by P. Zwart (1973)
P. Zwart, “Computational aspects of the use of cutting planes in global optimization”, in:Proceedings of the 1971 Annual Conference of the ACM (ACM, 1971) pp. 457–465. (10.1145/800184.810515)
P. Zwart, “Global maximization of a convex function with linear inequality constraints”,Operations Research 22(3) (1976) 602–609. (10.1287/opre.22.3.602) / Operations Research by P. Zwart (1976)

Dates

Type	When
Created	20 years, 4 months ago (April 28, 2005, 12:29 a.m.)
Deposited	6 years, 4 months ago (May 3, 2019, 7:12 a.m.)
Indexed	2 months ago (July 1, 2025, 7:06 a.m.)
Issued	44 years, 9 months ago (Dec. 1, 1980)
Published	44 years, 9 months ago (Dec. 1, 1980)
Published Print	44 years, 9 months ago (Dec. 1, 1980)

Funders 0

None

BibTeX

@article{Sherali_1980, title={A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts}, volume={19}, ISSN={1436-4646}, url={http://dx.doi.org/10.1007/bf01581626}, DOI={10.1007/bf01581626}, number={1}, journal={Mathematical Programming}, publisher={Springer Science and Business Media LLC}, author={Sherali, Hanif D. and Shetty, C. M.}, year={1980}, month=dec, pages={14–31} }

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