Anke Tröltzsch, PhD defense : June 7, 2011
An active-set trust-region method for bound-constrained nonlinear optimization without derivatives applied to noisy aerodynamic design problems
Anke TRÖLTZSCH
Tuesday June 7, 10.30 a.m. at CERFACS conference room
Jury
- L. N. VICENTE : Professor, University of Coimbra, Portugal (Referee)
- J. Ch. GILBERT: Directeur de recherche, INRIA Paris Rocquencourt, France (Referee)
- M. MEAUX: Engineer, Airbus, France
- B. MOHAMMADI: Directeur de laboratoire, CERFACS, France
- Ph. L. TOINT: Professor, University of Namur, Belgium (PhD co-advisor)
- S. GRATTON: Professor, ENSEEIHT,France (PhD advisor)
Abstract
Derivative-free optimization (DFO) has enjoyed renewed interest over the past years, mostly motivated by the ever growing need to solve optimization problems defined by functions whose values are computed by simulation (e.g. engineering design, medical image restoration or groundwater supply).
In the last few years, a number of derivative-free optimization methods have been developed where especially model-based trust-region methods have been shown to perform well. In this thesis, we present a new interpolation-based trust-region algorithm. The new algorithm relies on the technique of self-correcting geometry proposed by Scheinberg and Toint in 2010. In their theory, they advanced the understanding of the role of geometry in model-based DFO methods, in our work, we improve the efficiency of their method while maintaining its good theoretical convergence properties. We further examine the influence of different types of interpolation models on the performance of the new algorithm.
Furthermore, we extended this method to handle bound constraints by applying an activeset strategy. Considering an active-set method in bound-constrained model-based optimization creates the opportunity of saving a substantial amount of function evaluations. It allows to maintain smaller interpolation sets while proceeding optimization in lower dimensional subspaces. The resulting algorithm is shown to be numerically highly competitive. We present results on a test set of smooth problems from the CUTEr collection and compare to well-known state-of-the-art packages from different classes of DFO methods.
To report numerical experiments incorporating noise, we create a test set of noisy problems by adding perturbations to the set of smooth problems. The choice of noisy problems was guided by a desire to mimic simulation-based optimization problems. Finally, we will present results on a real-life application of a wing-shape design problem provided by Airbus.
