Abstract
A method of constructing test problems with known global solution for a class of reverse convex programs or linear programs with an additional reverse convex constraint is presented. The initial polyhedron is assumed to be a hypercube. The method then systematically generates cuts that slice the cube in such a way that a prespecified global solution on its edge remains intact. The proposed method does not require the solution of linear programs or systems of linear equations as is often required by existing techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bansal, P. P., andJacobsen, S. E.,Characterization of Basic Solutions for a Class of Nonconvex Programs, Journal of Optimization Theory and Applications, Vol. 15, pp. 549–564, 1975.
Bansal, P. P., andJacobsen, S. E.,An Algorithm for Optimizing Network Flow Capacity under Economies-of-Scale, Journal of Optimization Theory and Applications, Vol. 15, pp. 565–586, 1975.
Avriel, M., andWilliams, A. C.,Complementary Geometric Programming, SIAM Journal on Applied Mathematics, Vol. 19, pp. 125–141, 1970.
Avriel, M., andWilliams, A. C.,An Extension of Geometric Programming with Applications in Engineering Optimization, Journal of Engineering Mathematics, Vol. 5, pp. 187–194, 1971.
Rosen, J. B.,Iterative Solution of Nonlinear Optimal Control Problems, SIAM Journal on Control, Vol. 4, pp. 223–244, 1966.
Moshirvaziri, K.,Computational Methods for Linear Programs with an Additional Reverse Convex Constraint, PhD Dissertation, Electrical Engineering Department, University of California, Los Angeles, 1989.
Sung, Y., andRosen, J. B.,Global Minimum Test Problem Construction, Mathematical Programming, Vol. 24, pp. 353–355, 1982.
Kalantari, B., andRosen, J. B.,Construction of Large-Scale Global Minimum Concave Quadratic Test Problems, Journal of Optimization Theory and Applications, Vol. 48, pp. 303–313, 1986.
Ben-Saad, S. andJacobsen, S. E.,A Level Set Algorithm for a Class of Reverse Convex Programs, Annals of Operations Research, Vol. 25, pp. 19–42, 1990.
Pardalos, P. M.,Generation of Large-Scale Quadratic Programs for Use as Global Optimization Test Problems, ACM Transactions on Mathematical Software, Vol. 13, pp. 133–137, 1987.
Jacobsen, S. E., andMoshirvaziri, K.,An Edge-Search Algorithm and Test Problems for Linear Reverse Convex Programs (to appear).
Author information
Authors and Affiliations
Additional information
Communicated by M. Avriel
The author would like to thank Prof. S. E. Jacobsen for his valuable remarks on initial drafts of this paper and the referees for their constructive suggestions.
Rights and permissions
About this article
Cite this article
Moshirvaziri, K. Construction of test problems for a class of reverse convex programs. J Optim Theory Appl 81, 343–354 (1994). https://doi.org/10.1007/BF02191668
Issue Date:
DOI: https://doi.org/10.1007/BF02191668