skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Global smoothing and continuation for large-scale molecular optimization

Abstract

We discuss the formulation of optimization problems that arise in the study of distance geometry, ionic systems, and molecular clusters. We show that continuation techniques based on global smoothing are applicable to these molecular optimization problems, and we outline the issues that must be resolved in the solution of large-scale molecular optimization problems.

Authors:
;
Publication Date:
Research Org.:
Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
221915
Report Number(s):
MCS-P-539-1095; CONF-9507228-1
ON: DE96007028
DOE Contract Number:
W-31109-ENG-38
Resource Type:
Conference
Resource Relation:
Conference: IMA workshop on large scale optimization and applications, Minneapolis, MN (United States), 10-28 Jul 1995; Other Information: PBD: Oct 1995
Country of Publication:
United States
Language:
English
Subject:
55 BIOLOGY AND MEDICINE, BASIC STUDIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; MOLECULAR CLUSTERS; COMPUTER CALCULATIONS; MOLECULES; MOLECULAR BIOLOGY; ALGORITHMS; TRANSFORMATIONS; GAUSS FUNCTION

Citation Formats

More, J.J., and Wu, Zhijun. Global smoothing and continuation for large-scale molecular optimization. United States: N. p., 1995. Web.
More, J.J., & Wu, Zhijun. Global smoothing and continuation for large-scale molecular optimization. United States.
More, J.J., and Wu, Zhijun. 1995. "Global smoothing and continuation for large-scale molecular optimization". United States. doi:. https://www.osti.gov/servlets/purl/221915.
@article{osti_221915,
title = {Global smoothing and continuation for large-scale molecular optimization},
author = {More, J.J. and Wu, Zhijun},
abstractNote = {We discuss the formulation of optimization problems that arise in the study of distance geometry, ionic systems, and molecular clusters. We show that continuation techniques based on global smoothing are applicable to these molecular optimization problems, and we outline the issues that must be resolved in the solution of large-scale molecular optimization problems.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1995,
month =
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share:
  • This paper presents the authors` recent work on developing parallel algorithms and software for solving the global minimization problem for molecular conformation, especially protein folding. Global minimization problems are difficult to solve when the objective functions have many local minimizers, such as the energy functions for protein folding. In their approach, to avoid directly minimizing a ``difficult`` function, a special integral transformation is introduced to transform the function into a class of gradually deformed, but ``smoother`` or ``easier`` functions. An optimization procedure is then applied to the new functions successively, to trace their solutions back to the original function. Themore » method can be applied to a large class of nonlinear partially separable functions including energy functions for molecular conformation and protein folding. Mathematical theory for the method, as a special continuation approach to global optimization, is established. Algorithms with different solution tracing strategies are developed. Different levels of parallelism are exploited for the implementation of the algorithms on massively parallel architectures.« less
  • We directly exploit a new, more realistic paradigm for the iterative optimization process itself, wherein we return the best-ever solution found over the entire computation rather than the last-seen solution that is generated in the final iteration. We propose non-monotone, adaptive threshold methods which are self-tuning to the individual optimization instance. These methods allow efficient escape from local minimum solutions because the parameter (threshold or temperature) schedule is allowed to be highly non-monotone, in some sense {open_quotes}following{close_quotes} the algorithm`s knowledge of the cost surface. We propose strategies for bounded-time optimization, i.e., strategies which explicitly depend on the total computing timemore » allowed as well as the current stage of the optimization. We exploit a new {open_quotes}big valley{close_quotes} picture of structure in the optimization cost surface to generate effective initial states for the computation; these ideas greatly influence the implementation of {open_quotes}multi-start{close_quotes} strategies.« less
  • 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 smoothingmore » properties.« less
  • This paper discusses a generalization of the function transformation scheme for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global optimization is established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but {open_quote}smoother{close_quote} or {open_quotes}easier{close_quote} functions. An optimization procedure can then be applied to the new functions successively, to trace their solutions back to the original function. Two types of transformation are defined: isotropic and anisotropic. We show that both transformations can be applied to a large classmore » of nonlinear partially separable functions including energy functions for molecular conformation. Methods to compute the transformation for these functions are given.« less
  • Dynamical systems theory provides a powerful framework for understanding the behavior of complex evolving systems. However applying these ideas to large-scale dynamical systems such as discretizations of multi-dimensional PDEs is challenging. Such systems can easily give rise to problems with billions of dynamical variables, requiring specialized numerical algorithms implemented on high performance computing architectures with thousands of processors. This talk will describe LOCA, the Library of Continuation Algorithms, a suite of scalable continuation and bifurcation tools optimized for these types of systems that is part of the Trilinos software collection. In particular, we will describe continuation and bifurcation analysis techniquesmore » designed for large-scale dynamical systems that are based on specialized parallel linear algebra methods for solving augmented linear systems. We will also discuss several other Trilinos tools providing nonlinear solvers (NOX), eigensolvers (Anasazi), iterative linear solvers (AztecOO and Belos), preconditioners (Ifpack, ML, Amesos) and parallel linear algebra data structures (Epetra and Tpetra) that LOCA can leverage for efficient and scalable analysis of large-scale dynamical systems.« less