Abstract
This paper describes a technique for generating disjointly constrained bilinear programming test problems with known solutions and properties. The proposed construction technique applies a simple random transformation of variables to a separable bilinear programming problem that is constructed by combining disjoint low-dimensional bilinear programs.
Similar content being viewed by others
References
G. Gallo and A. Ülkücü, “Bilinear programming: an exact algorithm,” Math. Programming, vol. 12, pp. 173–194, 1977.
J. Judice and A. Faustino, “A computational analysis of LCP methods for bilinear and concave quadratic programming,” Comput. Oper. Res., vol. 18, pp. 645–654, 1991.
H. Konno, “Bilinear programming — Part II — Applications,” Dept. of Oper. Res. Tech. Report No. 71-10, Stanford Univ., 1971.
H. Konno, “A cutting plane algorithm for solving bilinear programs,” Math. Programming, vol. 11, pp. 14–27, 1976.
H. Konno, “Maximization of a convex quadratic function under linear constraints,” Math. Programming, vol. 11, pp. 117–127, 1976.
S. Sahni, “Computational related topics,” SIAM J. Comput., vol. 3, pp. 262–279, 1974.
H. Sherali and C. Shetty, “A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts” Math. Programming, vol. 19, pp. 14–31, 1980.
H. Vaish, “Nonconvex programming, with applications to production and location problem,” PhD thesis, Georgia Inst. of Tech., 1974 (unpublished).
H. Vaish and C. Shetty, “The bilinear programming problem,” Nav. Res. Logistics Q., vol. 23, pp. 303–309, 1976.
H. Vaish and C. Shetty, “A cutting plane algorithm for bilinear programming problem,” Nav. Res. Logistics Q., vol. 24, 83–94, 1977.
Y. Yajima and H. Konno, “Efficient algorithms for solving rank two and rank three bilinear programming problems,” J. of Global Optimization, vol. 1, pp. 155–171, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vicente, L.N., Calamai, P.H. & Júdice, J.J. Generation of disjointly constrained bilinear programming test problems. Comput Optim Applic 1, 299–306 (1992). https://doi.org/10.1007/BF00249639
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00249639