DocumentCode :
51942
Title :
Stability of Coupled Local Minimizers Within the Lagrange Programming Network Framework
Author :
Xuyang Lou ; Suykens, Johan A. K.
Author_Institution :
Key Lab. of Adv. Process Control for Light Ind. (Minist. of Educ.), Jiangnan Univ., Wuxi, China
Volume :
60
Issue :
2
fYear :
2013
fDate :
Feb. 2013
Firstpage :
377
Lastpage :
388
Abstract :
Coupled local minimizers (CLMs) turn out to be a potential global optimization strategy to explore a search space, avoid overfitting and produce good generalization. In this paper, convergence properties of CLMs based on an augmented Lagrangian function in the context of equality constrained minimization, are studied. We first consider the augmented Lagrangian by taking the objective of minimizing the average cost of an ensemble of local minimizers subject to pairwise synchronization constraints. Then we study an array of CLMs within the Lagrange programming network framework and analyze the local stability of CLMs using a linearization strategy. We further show that, under some mild conditions, global asymptotical stability of the unique equilibrium point of the network can be guaranteed. Afterwards, some sufficient conditions are presented to ensure the stability of synchronization between any two minimizers via a directed graph method. The results show that the CLMs usually can be synchronized if the penalty factors in the array of CLMs are chosen large enough. It is worth pointing out that CLMs possess the capability of global exploration in the search space and the advantage of faster running time on convex problems in comparison with most of the neural network approaches, which is also illustrated through two test functions and their numerical simulations.
Keywords :
circuit optimisation; linearisation techniques; CLM array; Lagrange programming network framework; augmented Lagrangian function; constrained minimization; convex problem; coupled local minimizer; directed graph method; global asymptotical stability; global exploration; global optimization strategy; linearization strategy; network equilibrium point; neural network approach; numerical simulation; pairwise synchronization constraint; test function; Asymptotic stability; Circuit stability; Neural networks; Optimization; Programming; Stability analysis; Synchronization; Coupled local minimizers; Lagrange programming network; augmented Lagrangian; stability; synchronization;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
Publisher :
ieee
ISSN :
1549-8328
Type :
jour
DOI :
10.1109/TCSI.2012.2215782
Filename :
6324398
Link To Document :
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