Globally Convergent Cutting Plane Method for Nonconvex Nonsmooth Minimization

Globally Convergent Cutting Plane Method for Nonconvex Nonsmooth Minimization

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Article ID: iaor20111977
Volume: 148
Issue: 3
Start Page Number: 528
End Page Number: 549
Publication Date: Mar 2011
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: heuristics, graphs
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, J. Optim. Theory Appl. 99(1):121–146, 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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