Abstract
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.
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Nesterov, Y.E., Nemirovskii, A.S. An interior-point method for generalized linear-fractional programming. Mathematical Programming 69, 177–204 (1995). https://doi.org/10.1007/BF01585557
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DOI: https://doi.org/10.1007/BF01585557