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Title: Implicitly and densely discrete black-box optimization problems
Authors: Vicente, L. N. 
Keywords: Derivative-free optimization; (dense) discrete optimization; Direct search; Projection; Rounding; Location; Grids
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-48 (2008)
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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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