Abstract
This paper is concerned with global minimization algorithms for solving rank-p linear fractional programming problems, namely the minimization of the sum of p(≥ 2) linear fractional functions over a polytope. Algorithms to be discussed are: parametric simplex algorithm for rank-2 problems, convergent approximate algorithm for rank-3 problems, generalized convex multiplicative programming approach and branch and bound algorithm using piecewise convex underestimating function. We will show that we are now able to obtain a globally optimal solution for up to rank-10 problems in a practical amount of time.
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Konno, H. (2001). Minimization of the Sum of Several Linear Fractional Functions. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_1
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DOI: https://doi.org/10.1007/978-3-642-56645-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41806-1
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