Abstract
Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.
Similar content being viewed by others
References
Charnes, A. and Cooper, W. W. (1962), Programming with Linear Fractional Functionals,Naval Research Logistics Quarterly 9, 181–186.
Falk, J. E. and Palocsay, S. W. (1994), Image Space Analysis of Generalized Fractional Programs,J. of Global Optimization 4, 63–88.
Horst, R. and Tuy, H. (1993),Global Optimization: Deterministic Approaches. Springer-Verlag, Berlin.
Konno, H. and Inori, M. (1988), Bond Portfolio Optimization by Bilinear Fractional Programming,Journal Operations Research Society of Japan 32, 143–158.
Konno, H. and Yajima, Y. (1992), Minimizing and Maximizing the Product of Linear Fractional Functions, eds. C. Floudas and M. Pardalos,Recent Advances in Global Optimization, 259–273.
Konno, H., Yajima, Y. and Matsui, T. (1991), Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems,Journal of Global Optimization 1, 65–81.
Kuno, T., Konno, H. and Yamamoto, Y. (1992), A Parametric Successive Underestimation Method for Convex Programming Problems with an Additional Convex Multiplicative Constraint,Journal Operations Research Society of Japan 35, 290–299.
Muu, Le D. and Oettli, W. (1991), A Method for Minimizing a Convex-Concave Function over a Convex Set,Journal of Optimization Theory and Applications 70, 337–384.
Muu, Le D. and Tam, B. T. (1992), Minimizing the Sum of a Convex Function and the Product of Two Affine Functions over a Convex Set,Optimization 24, 57–62.
Pardalos, P. M. (1990), Polynomial Time Algorithms for Some Classes of Constrained Nonconvex Quadratic Problems,Optimization 21, 843–853.
Thach, P. T., Burkard, R. E., and Oettli, W. (1991), Mathematical Programs with a Two-Dimensional Reverse Convex Constraint,Journal of Global Optimization 2, 145–154.
Tu, P. N. V. (1984),Introductory Optimization Dynamics, Springer-Verlag, Berlin.
Tuy, H. (1990), Polyhedral Annexation, Dualization and Dimension Reduction Technique in Global Optimization, preprint the Linköping Institute of Technology.
Tuy, H. and Tam, B. T. (1992), An Efficient Solution Method for Rank Two Quasi-Concave Minimization Problems,Optimization 24, 43–56.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Muu, L.D., Tam, B.T. & Schaible, S. Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions. J Glob Optim 6, 179–191 (1995). https://doi.org/10.1007/BF01096767
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01096767