Sven Leyffer, senior computational mathematician in Argonne National Laboratory’s Mathematics and Computer Science Division, and his colleagues Chungen Shen of Shanghai Finance University and Roger Fletcher of the University of Dundee received the 2012 Best Paper Prize for their paper “A nonmonotone filter method for nonlinear optimization.”
The paper, which appeared in the international journal Computational Optimization and Applications, was chosen by the editorial board from more than 130 papers. An article about the award-winning paper is featured in the November 2013 issue of the journal.
“Our aim was to develop a method that avoided the use of old filter entries that seemed to be preventing fast local convergence,” said Chungen, who did much of the research for the paper while he was visiting Argonne as a summer student.
The new strategy that the team developed switches between two filters: a global filter, which ensures convergence toward stationary points, and a nonmonotone local filter, which allows the algorithm to ignore outdated filter entries. The results show that it is possible to achieve proof of fast local convergence without the need for second-order correction steps — a requirement that has limited the effectiveness of former approaches.
“The two filters interact in a natural way,” said Leyffer. “We measure progress with the global filter. When the trust region becomes inactive, we start using the local filter until we get convergence. Or, if a step is not acceptable, we flush the local filter and return to using the global filter, backtracking to the last iterate that was acceptable.”
Results show that the new implementation, called FASTr (for filter active-set trust-region solver) outperforms filterSQP, a popular software package developed by Fletcher and Leyffer for solving nonlinear programming problems. The researchers attribute this improvement in part to the fact that the nonmonotonicity of FASTr allows more steps to be accepted, even far from the solution, resulting in faster convergence.
The award-winning paper “A nonmonotone filter method for nonlinear optimization,” Computational Optimization and Applications (2013) 56:503-506, is available on the web.