多集分裂等式问题的逐次松弛投影算法

doi:10.15960/j.cnki.issn.1007-6093.2021.02.007

Abstract

Abstract:

The multiple-sets split equality problem is an extended split feasibility problem, which has a wide application in image reconstruction, language processing, and seismic exploration. In order to solve this problem, we propose a successive relaxed projection algorithm with a variable stepsize which can fully use the information of the current iteration point and does not need the calculation of the operator norm. Furthermore the weak convergence of the algorithm is proved. The numerical examples show the superiority of the algorithm in the number of iterations and the running time.

Key words: multiple-sets split equality problem, successive relaxed projection algorithm, convergence

CLC Number:

O224

Xueling ZHOU, Meixia LI, Haitao CHE. Successive relaxed projection algorithm for multiple-sets split equality problem[J]. Operations Research Transactions, 2021, 25(2): 93-103.

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URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2021.02.007

https://www.ort.shu.edu.cn/EN/Y2021/V25/I2/93

Figures/Tables 4

References 20

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初始点	算法1	算法RTPPM
Case 1	$ n = 65; s = 0.025\;512 $ $ x^* = (-0.240, 0.092, 0.049)^\mathrm{T} $ $ y^* = (-0.130, 0.054, 0.009, 0.006)^\mathrm{T} $	$ n = 169; s = 0.003\;357 $ $ x^* = (-0.241, -0.037, 0.058)^\mathrm{T} $ $ y^* = (-0.073, 0.043, -0.022, -0.055)^\mathrm{T} $
Case 2	$ n = 172; s = 0.065\;433 $ $ x^* = (-0.016, -0.071, -0.002)^\mathrm{T} $ $ y^* = (0.008, -0.010, -0.018, -0.021)^\mathrm{T} $	$ n = 9\;464; s = 0.172\;677 $ $ x^* = (0.033, -0.074, -0.015)^\mathrm{T} $ $ y^* = (0.042, -0.006, -0.007, -0.037)^\mathrm{T} $
Case 3	$ n = 203; s = 0.075\;807 $ $ x^* = (-0.022, -0.096, -0.006)^\mathrm{T} $ $ y^* = (0.008, -0.015, -0.024, -0.027)^\mathrm{T} $	$ n = 36\;951; s = 0.644\;358 $ $ x^* = (0.074, -0.099, -0.053)^\mathrm{T} $ $ y^* = (0.044, -0.0179, 0.001, -0.035)^\mathrm{T} $
Case 4	$ n = 331; s = 0.115\;664 $ $ x^* = (0.036, 0.265, -0.097)^\mathrm{T} $ $ y^* = (-0.152, 0.019, 0.098, 0.140)^\mathrm{T} $	$ n = 40\;670; s = 0.773\;443 $ $ x^* = (0.158, 0.274, -0.134)^\mathrm{T} $ $ y^* = (-0.089, 0.022, 0.126, 0.124)^\mathrm{T} $

				算法1		算法RTPPM
	$ J $	$ N $	$ M $	$ n $	$ s $	$ n $	$ s $
	6	15	10	42	0.003 060	2 469	0.062 804
Case 1	10	20	30	52	0.002 697	9 349	0.308 245
	40	30	35	325	0.016 372	50 147	1.890 826
	$ 6 $	$ 15 $	$ 10 $	76	0.003 525	1 013	0.030 080
Case 2	10	20	30	48	0.003 492	2 896	0.098 542
	40	30	35	241	0.011 117	21 248	0.818 620
	$ 6 $	$ 15 $	$ 10 $	99	0.004 066	3 085	0.065 888
Case 3	10	20	30	52	0.003 352	9 317	0.319 493
	40	30	35	355	0.013 316	54 935	2.134 303
	$ 6 $	$ 15 $	$ 10 $	29	0.002 937	3 360	0.075 676
Case 4	10	20	30	49	0.002 736	9 423	0.326 474
	40	30	35	250	0.008 530	54 172	2.057 903

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Successive relaxed projection algorithm for multiple-sets split equality problem

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