Multi-funnel optimization using Gaussian underestimation

Roummel F. Marcia, Julie C. Mitchell, J. Ben Rosen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In several applications, underestimation of functions has proven to be a helpful tool for global optimization. In protein-ligand docking problems as well as in protein structure prediction, single convex quadratic underestimators have been used to approximate the location of the global minimum point. While this approach has been successful for basin-shaped functions, it is not suitable for energy functions with more than one distinct local minimum with a large magnitude. Such functions may contain several basin-shaped components and, thus, cannot be underfitted by a single convex underestimator. In this paper, we propose using an underestimator composed of several negative Gaussian functions. Such an underestimator can be computed by solving a nonlinear programming problem, which minimizes the error between the data points and the underestimator in the L 1 norm. Numerical results for simulated and actual docking energy functions are presented.

Original languageEnglish
Pages (from-to)39-48
Number of pages10
JournalJournal of Global Optimization
Volume39
Issue number1
DOIs
StatePublished - Sep 2007
Externally publishedYes

Funding

Acknowledgments This research was funded by the National Library of Medicine Training Grant 5T15LM007359-03, Department of Energy Grant DE-FG03-01ER25497, and NSF Grant #0513121.

FundersFunder number
National Science Foundation0513121
U.S. Department of EnergyDE-FG03-01ER25497
U.S. National Library of Medicine5T15LM007359-03

    Keywords

    • Gaussian functions
    • Nonlinear programming
    • Protein docking
    • Underestimators

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