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拉格朗日神經(jīng)網(wǎng)絡(luò)解決帶等式和不等式約束的非光滑非凸優(yōu)化問題

喻昕,  許治健,  陳昭蓉,  徐辰華

喻昕, 許治健, 陳昭蓉, 徐辰華. 拉格朗日神經(jīng)網(wǎng)絡(luò)解決帶等式和不等式約束的非光滑非凸優(yōu)化問題[J]. 電子與信息學(xué)報, 2017, 39(8): 1950-1955. doi: 10.11999/JEIT161049
引用本文: 喻昕, 許治健, 陳昭蓉, 徐辰華. 拉格朗日神經(jīng)網(wǎng)絡(luò)解決帶等式和不等式約束的非光滑非凸優(yōu)化問題[J]. 電子與信息學(xué)報, 2017, 39(8): 1950-1955. doi: 10.11999/JEIT161049
YU Xin, XU Zhijian, CHEN Zhaorong, XU Chenhua. Lagrange Neural Network for Nonsmooth Nonconvex Optimization Problems with Equality and Inequality Constrains[J]. Journal of Electronics & Information Technology, 2017, 39(8): 1950-1955. doi: 10.11999/JEIT161049
Citation: YU Xin, XU Zhijian, CHEN Zhaorong, XU Chenhua. Lagrange Neural Network for Nonsmooth Nonconvex Optimization Problems with Equality and Inequality Constrains[J]. Journal of Electronics & Information Technology, 2017, 39(8): 1950-1955. doi: 10.11999/JEIT161049

拉格朗日神經(jīng)網(wǎng)絡(luò)解決帶等式和不等式約束的非光滑非凸優(yōu)化問題

doi: 10.11999/JEIT161049
  • 1.

    (廣西大學(xué)計(jì)算機(jī)與電子信息學(xué)院 南寧 530004) ②(廣西大學(xué)電氣工程學(xué)院 南寧 530004)

基金項(xiàng)目: 

國家自然科學(xué)基金(61462006, 51407037)，廣西自然科學(xué)基金(2014GXNSFAA118391)

Lagrange Neural Network for Nonsmooth Nonconvex Optimization Problems with Equality and Inequality Constrains

  • 1.

    (School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China)

  • 2.

    (School of Electrical Engineering, Guangxi University, Nanning 530004, China)

Funds: 

The National Natural Science Foundation of China (61462006, 51407037), The Natural Science Foundation of Guangxi Province (2014GXNSFAA118391)

  • 摘要: 非凸非光滑優(yōu)化問題涉及科學(xué)與工程應(yīng)用的諸多領(lǐng)域，是目前國際上的研究熱點(diǎn)。該文針對已有基于早期罰函數(shù)神經(jīng)網(wǎng)絡(luò)解決非光滑優(yōu)化問題的不足，借鑒Lagrange乘子罰函數(shù)的思想提出一種有效解決帶等式和不等式約束的非凸非光滑優(yōu)化問題的遞歸神經(jīng)網(wǎng)絡(luò)模型。由于該網(wǎng)絡(luò)模型的罰因子是變量，無需計(jì)算罰因子的初始值仍能保證神經(jīng)網(wǎng)絡(luò)收斂到優(yōu)化問題的最優(yōu)解，因此更加便于網(wǎng)絡(luò)計(jì)算。此外，與傳統(tǒng)Lagrange方法不同，該網(wǎng)絡(luò)模型增加了一個等式約束懲罰項(xiàng)，可以提高網(wǎng)絡(luò)的收斂能力。通過詳細(xì)的分析證明了該網(wǎng)絡(luò)模型的軌跡在有限時間內(nèi)必進(jìn)入可行域，且最終收斂于關(guān)鍵點(diǎn)集。最后通過數(shù)值實(shí)驗(yàn)驗(yàn)證了所提出理論的有效性。
    Abstract: Nonconvex nonsmooth optimization problems are related to many fields of science and engineering applications, which are research hotspots. For the lack of neural network based on early penalty function for nonsmooth optimization problems, a recurrent neural network model is proposed using Lagrange multiplier penalty function to solve the nonconvex nonsmooth optimization problems with equality and inequality constrains. Since the penalty factor in this network model is variable, without calculating initial penalty factor value, the network can still guarantee convergence to the optimal solution, which is more convenient for network computing. Compared with the traditional Lagrange method, the network model adds an equality constraint penalty term, which can improve the convergence ability of the network. Through the detailed analysis, it is proved that the trajectory of the network model can reach the feasible region in finite time and finally converge to the critical point set. In the end, numerical experiments are given to verify the effectiveness of the theoretic results.
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出版歷程
  • 收稿日期:  2016-10-12
  • 修回日期:  2017-04-18
  • 刊出日期:  2017-08-19

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