4 research outputs found
A Simple Sufficient Descent Method for Unconstrained Optimization
We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient
at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed
method converges globally. Numerical experiments on some unconstrained minimization problems
from CUTEr library are reported, which illustrate that the proposed method is promising
The LBFGS Quasi-Newtonian Method for Molecular Modeling Prion AGAAAAGA Amyloid Fibrils
Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance)
spectroscopy, dual polarization interferometry, etc are indeed very powerful
tools to determine the 3-Dimensional structure of a protein (including the
membrane protein); theoretical mathematical and physical computational
approaches can also allow us to obtain a description of the protein 3D
structure at a submicroscopic level for some unstable, noncrystalline and
insoluble proteins. X-ray crystallography finds the X-ray final structure of a
protein, which usually need refinements using theoretical protocols in order to
produce a better structure. This means theoretical methods are also important
in determinations of protein structures. Optimization is always needed in the
computer-aided drug design, structure-based drug design, molecular dynamics,
and quantum and molecular mechanics. This paper introduces some optimization
algorithms used in these research fields and presents a new theoretical
computational method - an improved LBFGS Quasi-Newtonian mathematical
optimization method - to produce 3D structures of Prion AGAAAAGA amyloid
fibrils (which are unstable, noncrystalline and insoluble), from the potential
energy minimization point of view. Because the NMR or X-ray structure of the
hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the
model constructed by this paper can be used as a reference for experimental
studies on this region, and may be useful in furthering the goals of medicinal
chemistry in this field
A New Method with Sufficient Descent Property for Unconstrained Optimization
Recently, sufficient descent property plays an important role in the global convergence analysis of some iterative methods. In this paper, we propose a new iterative method for solving unconstrained optimization problems. This method provides a sufficient descent direction for objective function. Moreover, the global convergence of the proposed method is established under some appropriate conditions. We also report some numerical results and compare the performance of the proposed method with some existing methods. Numerical results indicate that the presented method is efficient