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Continuous Optimization Methods for Structure Alignments R. Andreani

Summary: Continuous Optimization Methods for Structure Alignments
R. Andreani
J. M. Mart´inez
L. Mart´inez §
F. Yano ¶
January 30, 2006 (Revised: April 18, 2006)
Structural Alignment is an important tool for fold identification of proteins, structural screen-
ing on ligand databases, pharmacophore identification and other applications. In the general
case, the optimization problem of superimposing two structures is nonsmooth and noncon-
vex, so that most popular methods are heuristic and do not employ derivative information.
Usually, these methods do not admit convergence theories of practical significance. In this
work it is shown that the optimization of the superposition of two structures may be ad-
dressed using continuous smooth minimization. It is proved that, using a Low Order-Value
Optimization approach, the nonsmoothness may be essentially ignored and classical opti-
mization algorithms may be used. Within this context, a Gauss-Newton method is intro-
duced for structural alignments incorporating (or not) transformations (as flexibility) on
the structures. Convergence theorems are provided and practical aspects of implementation
are described. Numerical experiments suggest that the Gauss-Newton methodology is com-
petitive with state-of-the-art algorithms for protein alignment both in terms of quality and


Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas


Collections: Mathematics