Variations on a cutting plane method for solving concave minimization problems with linear constraints. (English) Zbl 0348.90131


90C25 Convex programming
90C10 Integer programming
65K05 Numerical mathematical programming methods
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[1] Balas, Operations Research 19 pp 19– (1971)
[2] Balinski, Nav. Res. Log. Quart. 8 pp 41– (1961)
[3] Cabot, Operations Research 18 (1970)
[4] and , Management Models and Industrial Applications of Linear Programming (Wiley, N.Y., 1961).
[5] Linear Programming and Extensions (Princeton University Press, Princeton, N.J., 1963).
[6] Falk, Management Science 15 (1969)
[7] Glover, Operations Research 21 pp 123– (1973)
[8] Glover, Operations Research 21 pp 141– (1973)
[9] ”Mixed Integer Programming Algorithms for Site Selection and Other Fixed-Charge Problems Having Capacity Constraints,” Department of Operations Research Report No. 6, Stanford University, Palo Alto, California (1967).
[10] , and , ”Extreme Point Mathematical Programming,” Dalhousie University, ( Feb. 1970).
[11] Lawler, Operations Research 18 pp 699– (1966)
[12] ”Attempts to Calculate Global Solutions of Problems That May Have Local Minima,” School of Engineering and Applied Science, The George Washington University, Washington, D.C. · Zbl 0276.90049
[13] Murty, Operations Research 16 (1968)
[14] ”Concave Programming Under Linear Constraints,” Soviet Mathematics, 1437–1440 (1964). · Zbl 0132.40103
[15] ”New Cuts for a Special Class of 0–1 Integer Programs,” Research Report in Applied Mathematics and Systems Theory, Rice University, Houston, Texas ( Nov. 1968).
[16] ”Finite Pure Integer Programming Algorithms Employing Only Hyperspherically Deduced Cuts,” presented at 39th meeting of Operations Research Society of America, Dallas ( May 1971).
[17] ”Computational Aspects of the Use of Cutting Planes in Global Optimization,” Proceedings of the 1971 Annual Conference of the Association of Computing Machinery, Chicago 457–465 (1971).
[18] ”Nonlinear Programming: Counter-examples to Global Optimization Algorithms Proposed by Ritter and Tui,” Department of Applied Mathematics and Computer Sciences, Washington University, St. Louis, Mo.
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