zbMATH — the first resource for mathematics

An interior-point method for generalized linear-fractional programming. (English) Zbl 0857.90124
Summary: We develop an interior-point polynomial-time algorithm for a generalized linear-fractional problem. The latter problem can be regarded as a nonpolyhedral extension of the usual linear-fractional programming; typical example (which is of interest for control theory) is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables.

90C32 Fractional programming
Full Text: DOI
[1] S. Boyd and L. El Ghaoui, ”Method of centers for minimizing generalized eigenvalue,”Linear Algebra and Applications 188 (1993) 63–111 (Special Issue on Numerical Linear Algebra Methods in Control, Signals and Systems). · Zbl 0781.65051
[2] S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan,Linear Matrix Inequalities in System and Control Science, SIAM Studies in Applied Mathematics (SIAM, Philadelphia, PA, 1994). · Zbl 0816.93004
[3] S. Boyd and Q. Yang, ”Structured and simultaneous Lyapunov function for system stability problems,”International Journal of Control 49 (1989) 2215–2240. · Zbl 0683.93057
[4] R.W. Freund and F. Jarre, ”An interior-point method for convex fractional programming,” AT&T Numerical Analysis Manuscript No. 93-03, Bell Laboratories, Muray Hill, NJ, 1993.
[5] R.W. Freund and F. Jarre, ”An interior-point method for multi-fractional programs with convex constraints,” AT&T Numerical Analysis Manuscript No. 93-07, Bell Laboratories, Murray Hill, NJ, 1993.
[6] A.S. Nemirovskii, ”On an algorithm of Karmarkar’s type,”Izvestija AN SSSR, Tekhnitcheskaya Kibernetika 1 (1987) (in Russian).
[7] Yu. Nesterov and A. Nemirovskii,Interior-point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia, PA, 1994). · Zbl 0824.90112
[8] M.J. Todd and B.P. Burrell, ”An extension of Karmarkar’s algorithm for linear programming using dual variables,”Algorithmica 1 (1986) 409–424. · Zbl 0621.90048
[9] Y. Ye, ”On the von Neumann economic growth problem,” Working Paper Series No. 92-9, Department of Management Sciences, Univ. Iowa, Iowa City, IA, 1992.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.