Parallelization of the Discrete Gradient Method of Non-smooth Optimization and Its Applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

[1]  Adam Liwo,et al.  Efficient parallel algorithms in global optimization of potential energy functions for peptides, proteins, and crystals , 2000 .

[2]  Harold A. Scheraga.  The Multiple‐Minima Problem in Protein Folding , 1991 .

[3]  V. F. Demʹi︠a︡nov,et al.  Constructive nonsmooth analysis , 1995 .

[4]  P. Pardalos,et al.  Optimization in computational chemistry and molecular biology : local and global approaches , 2000 .

[5]  H. Scheraga,et al.  Global optimization of clusters, crystals, and biomolecules. , 1999, Science.

[6]  Philip Wolfe,et al.  Finding the nearest point in A polytope , 1976, Math. Program..

[7]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[8]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[9]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[10]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[11]  Adil M. Bagirov,et al.  A Method for Minimization of Quasidifferentiable Functions , 2002, Optim. Methods Softw..

[12]  Bernd Hartke,et al.  Global Geometry Optimization of Molecular Clusters: TIP4P Water , 2000 .

[13]  Arnold Neumaier,et al.  Molecular Modeling of Proteins and Mathematical Prediction of Protein Structure , 1997, SIAM Rev..

[14]  J. Doye,et al.  Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms , 1997, cond-mat/9803344.

[15]  Jay W. Ponder,et al.  Analysis and Application of Potential Energy Smoothing and Search Methods for Global Optimization , 1998 .

[16]  Fabio Schoen,et al.  Fast Global Optimization of Difficult Lennard-Jones Clusters , 2002, Comput. Optim. Appl..

[17]  Michael Allen,et al.  Parallel programming: techniques and applications using networked workstations and parallel computers , 1998 .

[18]  Christodoulos A. Floudas,et al.  Deterministic global optimization - theory, methods and applications , 2010, Nonconvex optimization and its applications.