# Concurrent Optimization with DUET: DIRECT Using External Trial Points

### Abstract

We consider the general problem of minimizing a real function subject to bound constraints. We are motivated by applications in which the derivatives of the objective function are unavailable or expensive to compute. This can occur, for example, when the function is not given analytically and is evaluated by running a simulation. The DIRECT algorithm by Jones, Pertunnen, and Stuckman is a global derivative-free optimization algorithm. It is a deterministic algorithm that samples the space following a scheme that is justifiable theoretically in case of Lipschitz continuous functions. In practice, DIRECT has proven to be efficient, with respect to the number of function evaluations, in finding a global minimum for a wide variety of functions. We extend the DIRECT algorithm to make use of additional free trial points that are made available when running DIRECT simultaneously with other optimization algorithms. We compare several deterministic and randomized variants of the DIRECT algorithm that use the external trial points (DUET). We present experimental results with external trial points that are sampled at random to show an improvement of DUET over the performance of the DIRECT algorithm.

Type
Publication
Tech. Rep., Sandia National Laboratories
Date
Tags
Citation
N. Goldberg, T. G. Kolda, A. S. Yoshimura. Concurrent Optimization with DUET: DIRECT Using External Trial Points. Tech. Rep. No. SAND2008-5844, Sandia National Laboratories, 2008.

### BibTeX

@techreport{SAND2008-5844,
author = {Noam Goldberg and Tamara G. Kolda and Ann S. Yoshimura},
title = {Concurrent Optimization with {DUET}: {DIRECT} Using External Trial Points},
number = {SAND2008-5844},
institution = {Sandia National Laboratories},
month = {September},
year = {2008},
}