The search functionality is under construction.

The search functionality is under construction.

A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrodinger-type equation, so global optimization is equivalent to eigen analysis of the Hamiltonian of a Schrodinger-type equation. Computer simulation of this method demonstrated that it produces a good approximation of the global optimum. An example optimization problem was solved using a Hamiltonian constructed by combining Hamiltonians for other optimization problems, demonstrating that various types of applications can be solved by combining simple Hamiltonians.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.8 pp.1476-1485

- Publication Date
- 2010/08/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E93.A.1476

- Type of Manuscript
- PAPER

- Category
- Nonlinear Problems

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

Copy

Hideki SATOH, "Global Nonlinear Optimization Based on Eigen Analysis of Schrodinger-Type Equation" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 8, pp. 1476-1485, August 2010, doi: 10.1587/transfun.E93.A.1476.

Abstract: A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrodinger-type equation, so global optimization is equivalent to eigen analysis of the Hamiltonian of a Schrodinger-type equation. Computer simulation of this method demonstrated that it produces a good approximation of the global optimum. An example optimization problem was solved using a Hamiltonian constructed by combining Hamiltonians for other optimization problems, demonstrating that various types of applications can be solved by combining simple Hamiltonians.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.1476/_p

Copy

@ARTICLE{e93-a_8_1476,

author={Hideki SATOH, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Global Nonlinear Optimization Based on Eigen Analysis of Schrodinger-Type Equation},

year={2010},

volume={E93-A},

number={8},

pages={1476-1485},

abstract={A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrodinger-type equation, so global optimization is equivalent to eigen analysis of the Hamiltonian of a Schrodinger-type equation. Computer simulation of this method demonstrated that it produces a good approximation of the global optimum. An example optimization problem was solved using a Hamiltonian constructed by combining Hamiltonians for other optimization problems, demonstrating that various types of applications can be solved by combining simple Hamiltonians.},

keywords={},

doi={10.1587/transfun.E93.A.1476},

ISSN={1745-1337},

month={August},}

Copy

TY - JOUR

TI - Global Nonlinear Optimization Based on Eigen Analysis of Schrodinger-Type Equation

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1476

EP - 1485

AU - Hideki SATOH

PY - 2010

DO - 10.1587/transfun.E93.A.1476

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E93-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2010

AB - A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrodinger-type equation, so global optimization is equivalent to eigen analysis of the Hamiltonian of a Schrodinger-type equation. Computer simulation of this method demonstrated that it produces a good approximation of the global optimum. An example optimization problem was solved using a Hamiltonian constructed by combining Hamiltonians for other optimization problems, demonstrating that various types of applications can be solved by combining simple Hamiltonians.

ER -