New Methods for Large Scale Local and Global Optimization
Final rept. 1 Dec 1991-30 Nov 1993
COLORADO UNIV AT BOULDER
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We have pursued all three topics described in the proposal during this research period. A large amount of effort has gone into the development of large scale global optimization methods for molecular configuration problems. We have developed new general purpose methods that combine efficient stochastic global optimization techniques with several new, more deterministic techniques that account for most of the computational effort, and the success, of the methods. We have applied our methods to Lennard-Jones problems with up to 75 atoms, to water clusters with up to 31, molecules, and polymers with up to 58 amino acids. The results appear to be the best so far by general purpose optimization methods, and appear to be leading to some interesting chemistry issues. Our research on the second topic, tensor methods, has addressed several areas. We have designed and implemented tensor methods for large sparse systems of nonlinear equations and nonlinear least squares, and have obtained excellent test results on a wide range of problems. We have also developed new tensor methods for nonlinearly constrained optimization problem, and have obtained promising theoretical and preliminary computational results. Finally, on the third topic, limited memory methods for large scale optimization, we have developed and implemented new, extremely efficient limited memory methods for bound constrained problems, and new limited memory trust regions methods, both using our-recently developed compact representations for quasi-Newton matrices. Computational test results for both methods are promising.
- Operations Research
- Atomic and Molecular Physics and Spectroscopy