Derivative-Free Optimization: Future Challenges and New Applications

Research grant PTDC/MAT/098214/2008 funded by FCT.

January 2010 - December 2012

Doctoral Members (core): Marc Baboulin, Ana Luísa Custódio, A. Ismael F. Vaz, and Luís Nunes Vicente (PI)
Doctoral Members (others): João Manuel Fernandes, Armindo Salvador, and Renata Silva
Graduate Students: Afonso Bandeira, Maria da Assunção Ferreira, Rohollah Garmanjani, and Alzira Teixeira da Mota
Consultants: Tiago Carvalho (GMV Lisbon), Benoit Colson (SamTech), Katya Scheinberg (Lehigh University), Michael Ulbrich (TU Munich), and Stefan Ulbrich (TU Darmstadt)

Optimization without derivatives finds numerous and increasing applications in the industry and in computational sciences. In part this is because of the growing sophistication of computer hardware and mathematical algorithms and software, which allows expensive simulations and opens new possibilities for optimization. On the other hand, we deal more frequently with binary codes (for which the source is unavailable or owned) and legacy codes (written in the past and no longer maintained). Thus, in many circumstances, the alternatives of Derivative-Free Optimization (DFO) cannot be applied: (i) derivatives are unavailable (e.g., absence of adjoint codes); (ii) the application of automatic differentiation is too complex or impossible; (iii) even when derivatives are available, the contamination by noise and the need to search for global minimizers make them useless.

The proposed work is organized around three main tasks: (i) Model-based methods (uncertainty, parallelization, constraints, multilevel DFO); (ii) Direct-search methods (global and multiobjective optimization & other issues); (iii) DFO in practice (the DFO applications of interest to us lie in computational systems biology, data mining and information science, and computational engineering for space technology).