Lyapunov Method for Solving Nonlinear Programming Problems Based on Control Ideas

doi:10.12068/j.issn.1005-3026.2021.09.001

Abstract

Abstract: In order to solve nonlinear programming problems efficiently， a novel optimization method named Lyapunov theory-based method (for short， Lyapunov method) based on control ideas is studied. This method transforms a constrained nonlinear programming problem into a dynamic system and presents optimal solution of the original optimization problem according to the dynamic characteristics of the system. Regarding to the single-objective and multi-objective nonlinear programming problems， the convergence of the algorithm is analyzed， and potential values of the key parameters such as the slack variables and gain factors in applications of the algorithm are suggested. A large number of numerical instances verify the aforementioned convergence and the correctness of the proposed parameter values， indicating the great potential and novelty of the method in solving nonlinear programming problems.

Key words: constrained nonlinear programming; multi-objective optimization; Lyapunov method; dynamic system; optimization algorithm

CLC Number:

TP18

ZHANG Rui-you， WANG Chao-hui， CHEN Yong-qiang. Lyapunov Method for Solving Nonlinear Programming Problems Based on Control Ideas[J]. Journal of Northeastern University(Natural Science), 2021, 42(9): 1217-1226.

References

[1]Fliege J，Drummond L M G，Svaiter B F.Newton′s method for multiobjective optimization［J］.SIAM Journal on Optimization，2009，20(2):602-626.
[2]Rao R V，Savsani V J，Vakharia D P.Teaching-learning-based optimization:an optimization method for continuous non-linear large scale problems［J］.Information Sciences，2012，183(1):1-15.
[3]Hu J，Jiang B，Lin L，et al.Structured quasi-Newton methods for optimization with orthogonality constraints［J］.SIAM Journal on Scientific Computing，2019，41(4):A2239-A2269.
[4]Liu X，Yuan Y.A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization［J］.SIAM Journal on Optimization，2011，21(2):545-571.
[5]Hong M，Luo Z Q，Razaviyayn M.Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems［J］.SIAM Journal on Optimization，2016，26(1):337-364.
[6]Li G，Pong T K.Global convergence of splitting methods for nonconvex composite optimization［J］.SIAM Journal on Optimization，2015，25(4):2434-2460.
[7]Han C，Wang L，Zhang Z L，et al.A multi-objective genetic algorithm based on fitting and interpolation［J］.IEEE Access，2018，6(1):22920-22929.
[8]Chen Y H，Zhang B.Multi-objective optimization of current limiting scheme based on NSGA-II［C］// Joint Conference of 6th International Congress on Electrical and Engineering(ICECE).Shanghai，2019:205-214.
[9]Gadhvi B，Savsani V，Patel V.Multi-objective optimization of vehicle passive suspension system using NSGA-II，SPEA2 and PESA-II［C］//3rd International Conference on Innovations in Automation and Mechatronics Engineering.Vallabh Vidhyanagar，2016:361-368.
[10]Torelli F，Vaccaro A，Xie N.A novel optimal power flow formulation based on the Lyapunov theory［J］.IEEE Transactions on Power Systems，2013，28(4):4405-4415.
[11]Torelli F，Montegiglio P，De Bonis A，et al.A new approach for solving DAE systems applied to distribution networks［C］// 49th International Universities Power Engineering Conference(UPEC).Cluj-Napoca，2014:131-139.

[1]	LI Chan， QU Lu-xuan， XIN Jun-chang， WANG Zhi-qiong. High-Order Dynamic Bayesian Network Modelling Method Based on Potential Regulatory Factors Screening [J]. Journal of Northeastern University(Natural Science), 2023, 44(3): 323-330.
[2]	ZHANG Zhi-min， QIAO Jian-zhong， LIN Shu-kuan， WANG Pin-he. A View Reconstruction Method Based on Deep Network [J]. Journal of Northeastern University Natural Science, 2020, 41(8): 1065-1069.
[3]	ZHAO Jian-zhe， WU Chen-ni， WANG Xing-wei， PEI Li-ya. Structure Learning Algorithm of Bayesian Networks Based on Markov Blanket [J]. Journal of Northeastern University Natural Science, 2020, 41(4): 464-470.
[4]	CUI Xue-ting， LI Ying， FAN Jia-hao. Global Chaotic Bat Optimization Algorithm [J]. Journal of Northeastern University Natural Science, 2020, 41(4): 488-492.
[5]	QU Lu-xuan， GUO Shang-hui， WANG Zhi-qiong， XIN Jun-chang. Modelling of Gene Regulatory Networks by Parent Node Screening-Based Bayesian Method [J]. Journal of Northeastern University Natural Science, 2020, 41(2): 158-162.
[6]	KONG Zhi， LI Shi-cheng， ZHAO Jie. Improved Coral Reef Algorithm [J]. Journal of Northeastern University Natural Science, 2020, 41(2): 163-169.
[7]	ZHAI Ying-ying， ZUO Li， ZHANG En-de. Algorithm for Structure Design of RBF Neural Network Based on Parameter Optimization [J]. Journal of Northeastern University Natural Science, 2020, 41(2): 176-182.
[8]	ZHANG Hua-wei， ZHENG Xiao-tao. Blank Holder Force Prediction of Tailor Welded Blank Based on Neural Network Optimized by Genetic Algorithm [J]. Journal of Northeastern University Natural Science, 2020, 41(2): 241-245.
[9]	YU Chang-yong， HE Xin， QI Xin， MA Hai-tao. GMSDenseNet:Lightweight DenseNet Based on Group Multi-structure Convolution [J]. Journal of Northeastern University Natural Science, 2020, 41(1): 12-16.
[10]	LI Zhan-shan， LIU Zhao-geng， YU Yin， YAN Wen-hao. A Quantized Pheromone Ant Colony Optimization Algorithm for Feature Selection [J]. Journal of Northeastern University Natural Science, 2020, 41(1): 17-22.
[11]	LI Zhuang， LIU Lei， ZHANG Tong-bo， LYU Shuai. Learnt Clauses Optimize Method Based on Restart Strategy [J]. Journal of Northeastern University Natural Science, 2020, 41(1): 44-48.
[12]	XU Lin， ZHENG Xiao-tong， FU Bo， TIAN Ge. Fault Diagnosis Method of Motor Bearing Based on Improved GAN Algorithm [J]. Journal of Northeastern University Natural Science, 2019, 40(12): 1679-1684.
[13]	MA Tie-min， ZHOU Fu-cai， WANG Shuang. Social Network Event Recommendation Algorithms Based on User Similarity Random Walk [J]. Journal of Northeastern University Natural Science, 2019, 40(11): 1533-1538.
[14]	JIANG Fang-fang， XU Jing-ao， LI Ren， XU Li-sheng. Automatic Detection Method of Paroxysmal Atrial Fibrillation for Ballistocardiagram Based on CNN [J]. Journal of Northeastern University Natural Science, 2019, 40(11): 1539-1543.
[15]	LIU Peng， DU Jia-zhi， LYU Wei-gang， DOU Ming-wu. A Modified KNN Classifier for Unbalanced Dataset [J]. Journal of Northeastern University Natural Science, 2019, 40(7): 932-936.