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Nonconvex Nonsmooth Minimization via Cutting Planes and Feasible Direction Interior Point Method

Napsu Karmitsa, Mario Tanaka, Jose Herskovits, Nonconvex Nonsmooth Minimization via Cutting Planes and Feasible Direction Interior Point Method. TUCS Technical Reports 960, Turku Centre for Computer Science, 2009.

Abstract:

Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper, we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines the traditional cutting plane method with some features of bundle methods, and the search direction calculation of feasible direction interior point algorithm [Herskovits 1998]. The algorithm to be presented generates a sequence of interior points to the epigraph of the objective
function. The accumulation points of this sequence are solutions to the original problem. We prove the global convergence of the method for locally Lipschitz continuous functions and give some preliminary results from numerical experiments.

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BibTeX entry:

@TECHREPORT{tKaTaHe09a,
  title = {Nonconvex Nonsmooth Minimization via Cutting Planes and Feasible Direction Interior Point Method},
  author = {Karmitsa, Napsu and Tanaka, Mario and Herskovits, Jose},
  number = {960},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2009},
  keywords = {Nondifferentiable programming, cutting planes, bundle methods, feasible direction interior point methods, nonconvex problems.},
  ISBN = {978-952-12-2369-3},
}

Belongs to TUCS Research Unit(s): Other

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