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Implicitely and Densely Discrete Black-Box Optimization Problems

L. N. Vicente(lnv***at***mat.uc.pt)

Abstract: This paper addresses derivative-free optimization problems where the variables lie implicitly in an unknown discrete closed set. The evaluation of the objective function follows a projection onto the discrete set, which is assumed dense rather than sparse. Such a mathematical setting is a rough representation of what is common in many real-life applications where, despite the continuous nature of the underlying models, a number of practical issues dictate rounding of values or projection to nearby feasible figures. We discuss a definition of minimization for these implicitly discrete problems and outline a direct search algorithm framework for its solution. The main asymptotic properties of the algorithm are analyzed and numerically illustrated.

Keywords: Derivative-free optimization, (dense) discrete optimization, direct search, projection, rounding, location, grids.

Category 1: Other Topics (Other )

Category 2: Nonlinear Optimization (Other )

Category 3: Integer Programming (Other )

Citation: Preprint 08-48, Dept. Mathematics, Univ. Coimbra

Download: [PDF]

Entry Submitted: 09/26/2008
Entry Accepted: 09/29/2008
Entry Last Modified: 09/26/2008

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