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Volume 22, Issue 1
An Algorithm for Finding Global Minimum of Nonlinear Integer Programming

Weiwen Tian & Liansheng Zhang

J. Comp. Math., 22 (2004), pp. 69-78.

Published online: 2004-02

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  • Abstract

A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear function using the above filled function is given. Meanwhile a major obstacle is met: if $ρ > 0$ is small, and $||x_I-\overset{*}{x}_I||$ is large, where $x_I$ - an integer point, $\overset{*}{x}_I$ - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled function and can not find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear function, and the new filled function improves some properties of the filled function proposed by R. Ge [2].
Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.

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@Article{JCM-22-69, author = {Tian , Weiwen and Zhang , Liansheng}, title = {An Algorithm for Finding Global Minimum of Nonlinear Integer Programming}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {69--78}, abstract = {

A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear function using the above filled function is given. Meanwhile a major obstacle is met: if $ρ > 0$ is small, and $||x_I-\overset{*}{x}_I||$ is large, where $x_I$ - an integer point, $\overset{*}{x}_I$ - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled function and can not find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear function, and the new filled function improves some properties of the filled function proposed by R. Ge [2].
Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10335.html} }
TY - JOUR T1 - An Algorithm for Finding Global Minimum of Nonlinear Integer Programming AU - Tian , Weiwen AU - Zhang , Liansheng JO - Journal of Computational Mathematics VL - 1 SP - 69 EP - 78 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10335.html KW - Local integer minimizer, Global integer minimizer, Filled function. AB -

A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear function using the above filled function is given. Meanwhile a major obstacle is met: if $ρ > 0$ is small, and $||x_I-\overset{*}{x}_I||$ is large, where $x_I$ - an integer point, $\overset{*}{x}_I$ - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled function and can not find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear function, and the new filled function improves some properties of the filled function proposed by R. Ge [2].
Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.

Weiwen Tian & Liansheng Zhang. (1970). An Algorithm for Finding Global Minimum of Nonlinear Integer Programming. Journal of Computational Mathematics. 22 (1). 69-78. doi:
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