Implicitly and densely discrete black-box optimization problems

• Author(s): Vicente, L. N.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11219
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Derivative-free optimization; (dense) discrete optimization; Direct search; Projection; Rounding; Location; Grids
• Document Type: Preprint
• Language: English

Description

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. FCT POCI/MAT/59442/2004, PTDC/MAT/64838/2006