A derivative-free optimization algorithm with subspace technique
 
 
Description:  We will talk about optimization algorithms that do not use derivatives, namely, derivative-free algorithms. We discuss how to incorporate subspace techniques into this type of algorithms, and present a new derivative-free algorithm with subspace techniques. For the new algorithm, we establish its global convergence and R-linear convergence rate; we propose a preconditioning technique, which improves the performance of our algorithm on ill-conditioned problems. We compare the new algorithm with the NEWUOA software, which is one of the state-of-the-art softwares. In the numerical experiments, our algorithm works evidently better than NEWUOA, in the number of function evaluations and CPU time. Besides, the new algorithm is capable of solving many 2000-dimensional test problems to high precision within several minutes, using not more than 50000 function evaluations (equivalent to less than 25 simplex gradients). Problems of this size are nearly unsolvable to most of the current derivative-free algorithms, including NEWUOA.
Date:  2012-10-03
Start Time:   11:30
Speaker:  Zaikun Zhang (Univ. Coimbra)
Institution:  FCT Research Grant PTDC/MAT/116736/2010
Place:  Room 5.5 (DMUC)
Research Groups: -Numerical Analysis and Optimization
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