scholarly journals Relaxed Successive Projection Algorithm with Strong Convergence for the Multiple-Sets Split Equality Problem

2017 ◽  
Vol 13 (5) ◽  
pp. 0-0
Author(s):  
Xueling Zhou ◽  
◽  
Meixia Li ◽  
Haitao Che ◽  
Keyword(s):  
Strong Convergence ◽  
Projection Algorithm ◽  
Split Equality Problem ◽  
Equality Problem ◽  
Successive Projection ◽  
Successive Projection Algorithm

Iterative algorithm for the split equality problem in Hilbert spaces

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Godwin Chidi Ugwunnadi
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Equality Problem ◽  
Equality Problem

AbstractIn this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed algorithm to solution of the split equality problems (SEP).

scholarly journals A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Haitao Che ◽  
Haibin Chen
Keyword(s):  
Fixed Point ◽  
Equation System ◽  
Projection Algorithm ◽  
Step Size ◽  
Split Equality Problem ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Equality Problem ◽  
Adaptive Step ◽  
Self Adaptive

In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

Least-squares support vector machine and successive projection algorithm for quantitative analysis of cotton-polyester textile by near infrared spectroscopy

2018 ◽  
Vol 26 (1) ◽  
pp. 34-43 ◽  
Author(s):  
Yisen Liu ◽  
Songbin Zhou ◽  
Weixin Liu ◽  
Xinhui Yang ◽  
Jun Luo
Keyword(s):  
Support Vector Machine ◽  
Infrared Spectroscopy ◽  
Least Squares ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Mean Squared Error ◽  
Projection Algorithm ◽  
Support Vector ◽  
Successive Projection ◽  
Successive Projection Algorithm

The application of near infrared spectroscopy for quantitative analysis of cotton-polyester textile was investigated in the present work. A total of 214 cotton-polyester fabric samples, covering the range from 0% to 100% cotton were measured and analyzed. Partial least squares and least-squares support vector machine models with all variables as input data were established. Furthermore, successive projection algorithm was used to select effective wavelengths and establish the successive projection algorithm-least-squares support vector machine models, with the comparison of two other effective wavelength selection methods: loading weights analysis and regression coefficient analysis. The calibration and validation results show that the successive projection algorithm-least-squares support vector machine model outperformed not only the partial least squares and least-squares support vector machine models with all variables as inputs, but also the least-squares support vector machine models with loading weights analysis and regression coefficient analysis effective wavelength selection. The root mean squared error of calibration and root mean squared error of prediction values of the successive projection algorithm-least-squares support vector machine regression model with the optimal performance were 0.77% and 1.17%, respectively. The overall results demonstrated that near infrared spectroscopy combined with least-squares support vector machine and successive projection algorithm could provide a simple, rapid, economical and non-destructive method for determining the composition of cotton-polyester textiles.

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