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A Simplified Convergence Proof for the Cone Partitioning Algorithm (1998)

Jaumard, Brigitte ; Meyer, Christophe

Springer

Journal of global optimization 13 (1998), S. 407-416

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ISSN: 1573-2916

Keywords: Cone partitioning ; Convergence ; ω-Subdivision ; (Quasi)concave minimization

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We present a new convergence result for the cone partitioning algorithm with a pure ω-subdivision strategy, for the minimization of a quasiconcave function over a polytope. It is shown that the algorithm is finite when ε-optimal solution with ε 〉 0 are looked for, and that any cluster point of the points generated by the algorithm is an optimal solution in the case ε = 0. This result improves on the one given previously by the authors, its proof is simpler and relies more directly on a new class of hyperplanes and its associated simplicial lower bound.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008325507949

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