Enclosure of all index-1 saddle points of general nonlinear functions
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Published version
Author(s)
Nerantzis, D
Adjiman, CS
Type
Journal Article
Abstract
Transition states (index-1 saddle points) play a crucial role in determining the rates of chemical transformations but their reliable identification remains challenging in many applications. Deterministic global optimization methods have previously been employed for the location of transition states (TSs) by initially finding all stationary points and then identifying the TSs among the set of solutions. We propose several regional tests, applicable to general nonlinear, twice continuously differentiable functions, to accelerate the convergence of such approaches by identifying areas that do not contain any TS or that may contain a unique TS. The tests are based on the application of the interval extension of theorems from linear algebra to an interval Hessian matrix. They can be used within the framework of global optimization methods with the potential of reducing the computational time for TS location. We present the theory behind the tests, discuss their algorithmic complexity and show via a few examples that significant gains in computational time can be achieved by using these tests.
Date Issued
2016-05-05
Online Publication Date
2016-05-05
Date Acceptance
2016-03-30
ISSN
1573-2916
Publisher
Springer Verlag (Germany)
Start Page
451
End Page
474
Journal / Book Title
Journal of Global Optimization
Volume
67
Issue
3
Copyright Statement
© The Author(s) 2016. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Source Database
manual-entry
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/J003840/1
Subjects
Science & Technology
Technology
Physical Sciences
Operations Research & Management Science
Mathematics, Applied
Mathematics
Global optimization
Transition states
Interval matrix
Eigenvalue bounding
NP-Hard
GLOBAL OPTIMIZATION METHOD
DIFFERENTIABLE CONSTRAINED NLPS
POTENTIAL-ENERGY SURFACES
ALPHA-BB
INTERVAL MATRICES
STATIONARY-POINTS
TRANSITION-STATES
STABILITY
EIGENVALUES
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Operations Research
Publication Status
Published