Convergence properties and stationary points of the two-layer backpropagation algorithm used for nonlinear function modeling

2002 ◽  
Author(s):  
M. Ibnkahla
Keyword(s):  
Nonlinear Function ◽  
Stationary Points ◽  
Convergence Properties ◽  
Backpropagation Algorithm

Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC

2018 ◽  
Vol 35 (01) ◽  
pp. 1850008
Author(s):  
Na Xu ◽  
Xide Zhu ◽  
Li-Ping Pang ◽  
Jian Lv
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Accumulation Point ◽  
Stationary Points ◽  
Nondegeneracy Condition ◽  
Equilibrium Constraints ◽  
Convergence Properties ◽  
Constant Rank Constraint Qualification ◽  
Relaxation Schemes

This paper concentrates on improving the convergence properties of the relaxation schemes introduced by Kadrani et al. and Kanzow and Schwartz for mathematical program with equilibrium constraints (MPEC) by weakening the original constraint qualifications. It has been known that MPEC relaxed constant positive-linear dependence (MPEC-RCPLD) is a class of extremely weak constraint qualifications for MPEC, which can be strictly implied by MPEC relaxed constant rank constraint qualification (MPEC-RCRCQ) and MPEC relaxed constant positive-linear dependence (MPEC-rCPLD), of course also by the MPEC constant positive-linear dependence (MPEC-CPLD). We show that any accumulation point of stationary points of these two approximation problems is M-stationarity under the MPEC-RCPLD constraint qualification, and further show that the accumulation point can even be S-stationarity coupled with the asymptotically weak nondegeneracy condition.

A Convergence Result for Learning in Recurrent Neural Networks

1994 ◽  
Vol 6 (3) ◽  
pp. 420-440 ◽  
Author(s):  
Chung-Ming Kuan ◽  
Kurt Hornik ◽  
Halbert White
Keyword(s):  
Neural Networks ◽  
Stochastic Processes ◽  
Recurrent Neural Networks ◽  
Convergence Result ◽  
Local Optimum ◽  
Recurrent Networks ◽  
Convergence Properties ◽  
Rigorous Analysis ◽  
Backpropagation Algorithm ◽  
Hidden Layer

We give a rigorous analysis of the convergence properties of a backpropagation algorithm for recurrent networks containing either output or hidden layer recurrence. The conditions permit data generated by stochastic processes with considerable dependence. Restrictions are offered that may help assure convergence of the network parameters to a local optimum, as some simulations illustrate.

scholarly journals Notes on Convergence Properties for a Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qingjie Hu ◽  
Yu Chen ◽  
Zhibin Zhu ◽  
Bishan Zhang
Keyword(s):  
Regularization Method ◽  
Accumulation Point ◽  
Stationary Points ◽  
Convergence Properties ◽  
Convergence Behavior ◽  
Mathematical Programs ◽  
Convergence Results ◽  
Vanishing Constraints ◽  
Regularization Problem ◽  
Strongly Stationary

We give some improved convergence results about the smoothing-regularization approach to mathematical programs with vanishing constraints (MPVC for short), which is proposed in Achtziger et al. (2013). We show that the Mangasarian-Fromovitz constraints qualification for the smoothing-regularization problem still holds under the VC-MFCQ (see Definition 5) which is weaker than the VC-LICQ (see Definition 7) and the condition of asymptotic nondegeneracy. We also analyze the convergence behavior of the smoothing-regularization method and prove that any accumulation point of a sequence of stationary points for the smoothing-regularization problem is still strongly-stationary under the VC-MFCQ and the condition of asymptotic nondegeneracy.

Convergence properties of hit-and-run samplers

1998 ◽  
Vol 14 (4) ◽  
pp. 767-800
Author(s):  
Claude Bélisle ◽  
Arnon Boneh ◽  
Richard J. Caron
Keyword(s):  
Convergence Properties ◽  
Hit And Run

Rancang Bangun Sistem Pakar Prediksi Stres Belajar Dengan Neural Network Algoritma Backpropagation

2016 ◽  
Vol 7 (2) ◽  
pp. 105-112
Author(s):  
Adhi Kusnadi ◽  
Idul Putra
Keyword(s):  
Neural Network ◽  
Expert System ◽  
Stress Level ◽  
Network Structure ◽  
Human Being ◽  
Accuracy Rate ◽  
Backpropagation Algorithm ◽  
Stress Prediction ◽  
Index Terms ◽  
Hidden Nodes

Stress will definitely be experienced by every human being and the level of stress experienced by each individual is different. Stress experienced by students certainly will disturb their study if it is not handled quickly and appropriately. Therefore we have created an expert system using a neural network backpropagation algorithm to help counselors to predict the stress level of students. The network structure of the experiment consists of 26 input nodes, 5 hidden nodes, and 2 the output nodes, learning rate of 0.1, momentum of 0.1, and epoch of 5000, with a 100% accuracy rate. Index Terms - Stress on study, expert system, neural network, Stress Prediction

Sign in / Sign up

Export Citation Format

Share Document