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Global optimization by equilibrium‐point search of gradient‐based dynamical system
Author(s) -
Masuda Kazuaki,
Kurihara Kenzo
Publication year - 2008
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.10026
Subject(s) - equilibrium point , nonlinear system , point (geometry) , mathematical optimization , optimization problem , computer science , dynamical system (definition) , gradient method , dynamical systems theory , nonlinear dynamical systems , mathematics , physics , geometry , quantum mechanics
Abstract This paper proposes a global optimization method based on thoroughly searching for equilibrium points of gradient‐based dynamical systems. Such a method is possible due to the linkage between equilibrium points of nonlinear systems and the outstanding properties of gradient dynamics. As the essence of this study, a general form of computational procedure for efficiently finding equilibrium points of nonlinear dynamical system based on the use of trajectories initiating from already known points into their eigendirections is provided. Then, optimization is realized by incorporating the procedure to gradient‐based models for obtaining various local optima as their stable equilibrium points. Its application to constrained global optimization is also discussed, and the effectiveness of our method is demonstrated through numerical simulations. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(1): 19– 31, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10026 Copyright © 2008