Generation of large-scale quadratic programs for use as global optimization test problems

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Generation of large-scale quadratic programs for use as global optimization test problems

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 13 , Issue 2 (June 1987) table of contents

Pages: 133 - 137

Year of Publication: 1987

ISSN:0098-3500

Author

Panos M. Pardalos

Pennsylvania State Univ., University Park

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 5, Downloads (12 Months): 22, Citation Count: 5

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ABSTRACT

A method is presented for the generation of test problems for global optimization algorithms. Given a bounded polyhedron in R and a vertex, the method constructs nonconvex quadratic functions (concave or indefinite) whose global minimum is attained at the selected vertex. The construction requires only the use of linear programming and linear systems of equations.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BIRKHOFF, G., AND GULATI, S. Isotropic distribution of test matrices. Z. Angew. Math. Phys. 30 (1979), 148-158.
	2	FALK, J. E., AND HOFFMAN, K.R. A successive underestimating method for concave minimization problems. Math. Oper. Res. I (1976), 251-259.
	3	B Kalantari , J B Rosen, Construction of large-scale global minimum concave quadratic test problems, Journal of Optimization Theory and Applications, v.48 n.2, p.303-313, Feb. 1986 [doi>10.1007/BF00940675]
	4	Melanie L. Lenard , Michael Minkoff, Randomly Generated Test Problems for Positive Definite Quadratic Programming, ACM Transactions on Mathematical Software (TOMS), v.10 n.1, p.86-96, March 1984 [doi>10.1145/356068.356075]
	5	PARDALOS, P.M. On generating test problems for global optimization algorithms. Rep. CS-86- 01, Computer Science Dept., Pennsylvania State Univ., University Park, 1986.
	6	P M Pardalos , J B Rosen, Methods for global concave minimization: A bibliographic survey, SIAM Review, v.28 n.3, p.367-379, Sept. 1986 [doi>10.1137/1028106]
	7	J B Rosen , P M Pardolas, Global minimization of large-scale constrained concave quadratic problems by separable programming, Mathematical Programming: Series A and B, v.34 n.2, p.163-174, March 1986 [doi>10.1007/BF01580581]
	8	STEWART, G.W. The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM J. Numer. Anal. 17 (1981), 403-409.
	9	SUNG, Y. Y., AND ROSEN, J.B. Global minimum test problem construction. Math. Program. 24 (1982), 353-355.

CITED BY 5

	Panos M. Pardalos, Construction of test problems in quadratic bivalent programming, ACM Transactions on Mathematical Software (TOMS), v.17 n.1, p.74-87, March 1991
	B. N. Khoury , P. M. Pardalos , D.-Z. Du, A test problem generator for the Steiner problem in graphs, ACM Transactions on Mathematical Software (TOMS), v.19 n.4, p.509-522, Dec. 1993
	Marco Gaviano , Dmitri E. Kvasov , Daniela Lera , Yaroslav D. Sergeyev, Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization, ACM Transactions on Mathematical Software (TOMS), v.29 n.4, p.469-480, December 2003
	Bernardetta Addis , Marco Locatelli, A new class of test functions for global optimization, Journal of Global Optimization, v.38 n.3, p.479-501, July 2007
	M. Gaviano , D. Lera, Test Functions with Variable Attraction Regions for GlobalOptimization Problems, Journal of Global Optimization, v.13 n.2, p.207-223, September 1998