Parameter-related projection-based iterative algorithm for a kind of generalized positive semidefinite least squares problem

Chengjin Li

doi:10.3934/naco.2020048

Article Contents

2020, Volume 10, Issue 4: 511-520. Doi: 10.3934/naco.2020048

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Parameter-related projection-based iterative algorithm for a kind of generalized positive semidefinite least squares problem

Chengjin Li

College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350007, P. R. China

Received: February 29, 2020

Revised: August 31, 2020

Published: September 2020

This work was supported by the National Natural Science Foundations of China (11301080, 11526053), Science Foundation of Fujian Province of China (2016J05003), the Foundation of the Education Department of Fujian Province of China (JA15106), and the Project of Nonlinear analysis and its applications (IRTL1206)

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Abstract

A projection-based iterative algorithm, which is related to a single parameter (or the multiple parameters), is proposed to solve the generalized positive semidefinite least squares problem introduced in this paper. The single parameter (or the multiple parameters) projection-based iterative algorithms converges to the optimal solution under certain condition, and the corresponding numerical results are shown too.

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Mathematics Subject Classification: Primary: 65K05; Secondary: 90C30.

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Table . Comparing of Algorithm 2.4 and Algorithm 3.2

Parameters		Spending time		Parameters		Spending time
$ (m,n,p,(r)) $	$ type $	$ tim1 $	$ tim2 $	$ (m,n,p,(r)) $	$ type $	$ tim1 $	$ tim2 $
(71, 65, 67)	T1	62.1	15.6	(59, 8, 30)	T1	0.017	0.016
(53, 39, 48)		2.13	1.95	(103, 61, 85)		1.82	1.09
(101, 33, 61)		0.25	0.19	(102, 78, 90)		8.95	5.61
(102, 19, 95)		0.040	0.039	(93, 20, 92)		0.041	0.038
(66, 48, 53)		10.1	3.28	(58, 18, 45)		0.05	0.05
(62, 4, 38)	T2	0.009	0.008	(49, 41, 42)	T2	115.6	8.67
(71, 11, 24)		0.04	0.02	(94, 44, 92)		0.94	0.28
(92, 43, 64)		1.99	0.45	(98, 19, 93)		0.05	0.03
(93, 7, 48)		0.014	0.012	(73, 4, 30)		0.008	0.007
(86, 64, 72)		32.9	3.99	(78, 39, 62)		1.54	0.34
(94, 16, 85, (6))	T3	0.03	0.02	(91, 43, 83, (21))	T3	0.90	0.20
(60, 36, 53, (25))		1.18	0.28	(54, 11, 24, (9))		0.04	0.02
(31, 8, 10, (7))		0.12	0.03	(86, 9, 83, (1))		0.019	0.015
(78, 55, 69, (7))		20.7	0.77	(97, 17, 33, (15))		0.08	0.04
(98, 43, 51, (3))		10.3	0.44	(42, 10, 36, (9))		0.023	0.019

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