Performance of Enriched Methods for Large Scale Unconstrained Optimization as applied to Models of Proteins

Energy minimization plays an important role in structure determination and analysis of proteins, peptides and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently Morales and Nocedal have developed enriched methods for large scale unconstrained optimization that interlace iterations of the limited memory BFGS method (L-BFGS) and the Hessian-free Newton method (Computational Optimization and Applications (2002) 21, 143-154). We test the performance of this approach as compared to those of the L-BFGS algorithm of Liu and Nocedal and the truncated Newton (TN) with automatic preconditioner of Nash, as applied to the protein bovine pancreatic trypsin inhibitor (BPTI) and a loop of the protein Ribonuclease A. These systems are described by the all-atom AMBER force field with a dielectric constant ε=1 and a distance dependent dielectric constant ε=2r, where r is the distance between two atoms. It is shown that for the optimal parameters, the hybrid approach is typically 2 times more efficient in terms of CPU time and function/gradient calculations than the two other methods. The advantage of the hybrid approach increases as the non-linearity of the energy function is enhanced, i.e., in going from ε=2r to ε=1, where the electrostatic interactions are stronger. However, no general rule that defines the optimal parameters has been found and their determination requires a relatively large number of trial and error calculations for each problem.