A Generalized Global Convergence Theory of Projection-Type Neural Networks for Optimization

2005 ◽  
pp. 777-784
Author(s):  
Rui Zhang ◽  
Zongben Xu
Keyword(s):  
Neural Networks ◽  
Global Convergence ◽  
Convergence Theory

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Convergence Theory for Unified Discrete-Time RNNs with Quasi-Symmetric Connection

2014 ◽  
Vol 538 ◽  
pp. 167-170
Author(s):  
Hui Zhong Mao ◽  
Chen Qiao ◽  
Wen Feng Jing ◽  
Xi Chen ◽  
Jin Qin Mao
Keyword(s):  
Neural Network ◽  
Global Convergence ◽  
Discrete Time ◽  
Recurrent Neural Network ◽  
Symmetric Matrix ◽  
Network Models ◽  
Convergence Theory ◽  
Connection Matrix ◽  
Neural Network Models ◽  
Symmetric Connection

This paper presents the global convergence theory of the discrete-time uniform pseudo projection anti-monotone network with the quasi–symmetric matrix, which removes the connection matrix constraints. The theory widens the range of applications of the discrete–time uniform pseudo projection anti–monotone network and is valid for many kinds of discrete recurrent neural network models.

Boundedness and global convergence of non-autonomous neural networks with variable delays

2009 ◽  
Vol 10 (4) ◽  
pp. 2195-2206 ◽  
Author(s):  
Zhaohui Yuan ◽  
Lifen Yuan ◽  
Lihong Huang ◽  
Dewen Hu
Keyword(s):  
Neural Networks ◽  
Global Convergence ◽  
Variable Delays
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