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Finiteness of conical algorithms with ω-subdivisions

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Abstract.

In this paper the problem of finding the global optimum of a concave function over a polytope is considered. A well-known class of algorithms for this problem is the class of conical algorithms. In particular, the conical algorithm based on the so called ω-subdivision strategy is considered. It is proved that, for any given accuracy ε>0, this algorithm stops in a finite time by returning an ε-optimal solution for the problem, while it is convergent for ε=0.

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Received January 24, 1996 / Revised version received December 9, 1998 Published online June 11, 1999

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Locatelli, M. Finiteness of conical algorithms with ω-subdivisions. Math. Program. 85, 593–616 (1999). https://doi.org/10.1007/s101070050073

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  • DOI: https://doi.org/10.1007/s101070050073

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