拉格朗日神經(jīng)網(wǎng)絡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

doi:10.11999/JEIT161049

拉格朗日神經(jīng)網(wǎng)絡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 cstr: 32379.14.JEIT161049

1.
(廣西大學計算機與電子信息學院南寧 530004) ②(廣西大學電氣工程學院南寧 530004)

基金項目:

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

計量
- 文章訪問數(shù): 2377
- HTML全文瀏覽量: 269
- PDF下載量: 346
- 被引次數(shù): 0
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

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

摘要: 非凸非光滑優(yōu)化問題涉及科學與工程應用的諸多領域，是目前國際上的研究熱點。該文針對已有基于早期罰函數(shù)神經(jīng)網(wǎng)絡解決非光滑優(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)絡模型。由于該網(wǎng)絡模型的罰因子是變量，無需計算罰因子的初始值仍能保證神經(jīng)網(wǎng)絡收斂到優(yōu)化問題的最優(yōu)解，因此更加便于網(wǎng)絡計算。此外，與傳統(tǒng)Lagrange方法不同，該網(wǎng)絡模型增加了一個等式約束懲罰項，可以提高網(wǎng)絡的收斂能力。通過詳細的分析證明了該網(wǎng)絡模型的軌跡在有限時間內(nèi)必進入可行域，且最終收斂于關鍵點集。最后通過數(shù)值實驗驗證了所提出理論的有效性。
- 拉格朗日神經(jīng)網(wǎng)絡 /
- 收斂 /
- 非凸非光滑優(yōu)化
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.
- Lagrange neural network /
- Convergence /
- Nonsmooth nonconvex optimization

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參考文獻(9)

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