Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 69, Issue 2, Pages 387-426Publisher
SPRINGER
DOI: 10.1007/s10898-017-0523-z
Keywords
Fractional programming; Generalized Huard's method of centers; Duality; Convergence; Rate of convergence
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In this paper we analyze the method of centers for generalized fractional programs, with further insights. The introduced method is based on a different parametric auxiliary problem than Dinkelbach's type. With the help of this auxiliary parametric problem, we present a new dual for convex generalized fractional programs. We then propose an algorithm to solve this problem, and subsequently the original primal program. The proposed algorithm generates a sequence of dual values that converges from below to the optimal value. The method also generates a bounded sequence of dual solutions whose every accumulation point is a solution of the dual problem. The rate of convergence is shown to be at least linear. In the penultimate section, we specialize the results obtained for the linear case. The computational results show that the different variants of our algorithms, primal as well as dual, are competitive.
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