Smoothing techniques for macromolecular global optimization

We study global optimization problems that arise in macromolecular modeling, and the solution of these problems via continuation and smoothing. Our results unify and extend the theory associated with the use of the Gaussian transform for smoothing. We show that the, Gaussian transform can be viewed as a special case of a generalized transform and that these generalized transforms share many of the properties of the Gaussian transform. We also show that the smoothing behavior of the generalized transform can be studied in terms of the Fourier transform and that these results indicate that the Gaussian transform has superior smoothing properties.

[1]  A. Stroud,et al.  Gaussian quadrature formulas , 1966 .

[2]  Philip Rabinowitz,et al.  Methods of Numerical Integration , 1985 .

[3]  E. M. Gelbard,et al.  Gaussian quadratures for the integrals ₀^{∞}(-²)() and ₀^{}(-²)() , 1969 .

[4]  E. M. Gelbard,et al.  Gaussian quadratures for the integrals $\sb{0}\sp{\infty }\,{\rm exp}(-x\sp{2})f(x)dx$ and $\sb{0}\sp{b}\,{\rm exp}(-x\sp{2})f(x)dx$ , 1969 .

[5]  A. Griewank.  Generalized descent for global optimization , 1981 .

[6]  J. Hammersley.  SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[7]  Reuven Y. Rubinstein,et al.  Smoothed Functionals in Stochastic Optimization , 1983, Math. Oper. Res..

[8]  Philip J. Davis,et al.  Chapter 6 – Automatic Integration , 1984 .

[9]  Reuven Y. Rubinstein,et al.  Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks , 1986 .

[10]  M. J. Norman,et al.  Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks , 1987 .

[11]  Gordon M. Crippen,et al.  Distance Geometry and Molecular Conformation , 1988 .

[12]  I. Kuntz,et al.  Distance geometry. , 1989, Methods in enzymology.

[13]  G. Rappl.  On Linear Convergence of a Class of Random Search Algorithms , 1989 .

[14]  I. Kuntz,et al.  [9] Distance geometry , 1989 .

[15]  H. Scheraga,et al.  On the multiple-minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method , 1989 .

[16]  J. Schiffer,et al.  The Structure of the Cylindrically Confined Coulomb Lattice , 1990 .

[17]  H. Scheraga,et al.  Performance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms , 1991 .

[18]  J. Kostrowicki,et al.  Diffusion equation method of global minimization: Performance for standard test functions , 1991 .

[19]  J S Hangst,et al.  Stable configurations of confined cold ionic systems. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Timothy F. Havel.  An evaluation of computational strategies for use in the determination of protein structure from distance constraints obtained by nuclear magnetic resonance. , 1991, Progress in biophysics and molecular biology.

[21]  David Shalloway,et al.  Packet annealing: a deterministic method for global minimization , 1992 .

[22]  David Shalloway,et al.  Application of the renormalization group to deterministic global minimization of molecular conformation energy functions , 1992, J. Glob. Optim..

[23]  Reuven Y. Rubinstein,et al.  Nondifferentiable optimization via smooth approximation: General analytical approach , 1992, Ann. Oper. Res..

[24]  Schiffer.  Phase transitions in anisotropically confined ionic crystals. , 1993, Physical review letters.

[25]  M. Nilges,et al.  Computational challenges for macromolecular structure determination by X-ray crystallography and solution NMRspectroscopy , 1993, Quarterly Reviews of Biophysics.

[26]  Thomas F. Coleman,et al.  Isotropic effective energy simulated annealing searches for low energy molecular cluster states , 1993, Comput. Optim. Appl..

[27]  Thomas F. Coleman,et al.  A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing , 1993, J. Glob. Optim..

[28]  WALTER GAUTSCHI.  Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules , 1994, TOMS.

[29]  Jorge J. Moré,et al.  E-optimal solutions to distance geometry problems via global continuation , 1995, Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding.

[30]  Y. Ermoliev,et al.  The Minimization of Semicontinuous Functions: Mollifier Subgradients , 1995 .

[31]  Zhijun Wu,et al.  The Eeective Energy Transformation Scheme as a General Continuation Approach to Global Optimization with Application to Molecular Conformation , 2022 .

[32]  John E. Straub,et al.  OPTIMIZATION TECHNIQUES WITH APPLICATIONS TO PROTEINS , 1996 .

[33]  Jorge J. Moré,et al.  Global Continuation for Distance Geometry Problems , 1995, SIAM J. Optim..