Piece adding technique for convex maximization problems

  • Authors:

  • Dominique Fortin;Ider Tseveendorj

  • Affiliations:

  • INRIA, Le Chesnay Cedex, France 78153;Laboratoire PRiSM, Université de Versailles, Versailles Cedex, France 78035

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2010

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Abstract

In this article we provide an algorithm, where to escape from a local maximum y of convex function f over D, we (locally) solve piecewise convex maximization max{min{f (x) 驴 f (y), p y (x)} | x 驴 D} with an additional convex function p y (·). The last problem can be seen as a strictly convex improvement of the standard cutting plane technique for convex maximization. We report some computational results, that show the algorithm efficiency.