ISSN:
1573-2878
Keywords:
Multifractional programming
;
convex sets
;
interior-point methods
;
self-concordant barrier functions
;
short-step algorithms
;
polynomial-time convergence
;
predictor-corrector step
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We present an interior-point method for a family of multi-fractional programs with convex constraints. The programs under consideration consist of minimizing the maximum of a finite number of linear fractions over some convex set. First, we present a simple shortstep algorithm for solving such multifractional programs, and we show that, under suitable assumptions, the convergence of the short-step algorithm is weakly polynomial in a sense specified below. Then, we describe a practical implementation of the proposed method, and we report results of numerical experiments with this algorithm. These results suggest that the proposed method is a viable alternative to the standard Dinkelbach-type algorithms for solving multifractional programs.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192302
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