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A method was developed for deriving the approximate global optimum of a nonlinear objective function with multiple local optimums. The objective function is expanded into a linear wave coefficient equation, so the problem of maximizing the objective function is reduced to that of maximizing a quadratic function with respect to the wave coefficients. Because a wave function expressed by the wave coefficients is used in the algorithm for maximizing the quadratic function, the algorithm is equivalent to a full search algorithm, i.e., one that searches in parallel for the global optimum in the whole domain of definition. Therefore, the global optimum is always derived. The method was evaluated for various objective functions, and computer simulation showed that a good approximation of the global optimum for each objective function can always be obtained.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.1 pp.291-301

- Publication Date
- 2010/01/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.291

- Type of Manuscript
- PAPER

- Category
- Nonlinear Problems

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Hideki SATOH, "Global Nonlinear Optimization Based on Wave Function and Wave Coefficient Equation" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 1, pp. 291-301, January 2010, doi: 10.1587/transfun.E93.A.291.

Abstract: A method was developed for deriving the approximate global optimum of a nonlinear objective function with multiple local optimums. The objective function is expanded into a linear wave coefficient equation, so the problem of maximizing the objective function is reduced to that of maximizing a quadratic function with respect to the wave coefficients. Because a wave function expressed by the wave coefficients is used in the algorithm for maximizing the quadratic function, the algorithm is equivalent to a full search algorithm, i.e., one that searches in parallel for the global optimum in the whole domain of definition. Therefore, the global optimum is always derived. The method was evaluated for various objective functions, and computer simulation showed that a good approximation of the global optimum for each objective function can always be obtained.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.291/_p

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@ARTICLE{e93-a_1_291,

author={Hideki SATOH, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Global Nonlinear Optimization Based on Wave Function and Wave Coefficient Equation},

year={2010},

volume={E93-A},

number={1},

pages={291-301},

abstract={A method was developed for deriving the approximate global optimum of a nonlinear objective function with multiple local optimums. The objective function is expanded into a linear wave coefficient equation, so the problem of maximizing the objective function is reduced to that of maximizing a quadratic function with respect to the wave coefficients. Because a wave function expressed by the wave coefficients is used in the algorithm for maximizing the quadratic function, the algorithm is equivalent to a full search algorithm, i.e., one that searches in parallel for the global optimum in the whole domain of definition. Therefore, the global optimum is always derived. The method was evaluated for various objective functions, and computer simulation showed that a good approximation of the global optimum for each objective function can always be obtained.},

keywords={},

doi={10.1587/transfun.E93.A.291},

ISSN={1745-1337},

month={January},}

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TY - JOUR

TI - Global Nonlinear Optimization Based on Wave Function and Wave Coefficient Equation

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 291

EP - 301

AU - Hideki SATOH

PY - 2010

DO - 10.1587/transfun.E93.A.291

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 1

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - January 2010

AB - A method was developed for deriving the approximate global optimum of a nonlinear objective function with multiple local optimums. The objective function is expanded into a linear wave coefficient equation, so the problem of maximizing the objective function is reduced to that of maximizing a quadratic function with respect to the wave coefficients. Because a wave function expressed by the wave coefficients is used in the algorithm for maximizing the quadratic function, the algorithm is equivalent to a full search algorithm, i.e., one that searches in parallel for the global optimum in the whole domain of definition. Therefore, the global optimum is always derived. The method was evaluated for various objective functions, and computer simulation showed that a good approximation of the global optimum for each objective function can always be obtained.

ER -