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Convergence Analysis of the DIRECT Algorithm

D. E. Finkel (definkel***at***unity.ncsu.edu)
C. T. Kelley (tim_kelley***at***ncsu.edu)

Abstract: The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from nonsmooth analysis, and our framework is based on recent results for the MADS sampling algorithms.

Keywords: DIRECT, Sampling Methods, Clarke derivative, Lipschitz Functions

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Unpublished: N. C. State University Center for Research in Scientific Computation Tech Report number CRSC-TR04-28, July, 2004

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Entry Submitted: 08/10/2004
Entry Accepted: 08/13/2004
Entry Last Modified: 08/10/2004

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