American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Pricing credit derivatives under a correlated regime-switching hazard processes model
  • JIMO Home
  • This Issue
  • Next Article
    Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy
July  2017, 13(3): 1383-1394. doi: 10.3934/jimo.2016078

Inertial accelerated algorithms for solving a split feasibility problem

Yazheng Dang 1,, , Jie Sun 2, and  Honglei Xu 2,

1. 

School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
2. 

Department of Mathematics and Statistics, Curtin University, Perth, WA 6102, Australia

* Corresponding author:Yazheng Dang. The reviewing process of the paper was handled by Changzhi Wu as a Guest Editor

Received  February 2015 Published  October 2016

Inspired by the inertial proximal algorithms for finding a zero of a maximal monotone operator, in this paper, we propose two inertial accelerated algorithms to solve the split feasibility problem. One is an inertial relaxed-CQ algorithm constructed by applying inertial technique to a relaxed-CQ algorithm, the other is a modified inertial relaxed-CQ algorithm which combines the KM method with the inertial relaxed-CQ algorithm. We prove their asymptotical convergence under some suitable conditions. Numerical results are reported to show the effectiveness of the proposed algorithms.

Keywords: Asymptotical convergence, inertial technique, nonsmooth analysis, split feasibility problem, subdifferential.
Mathematics Subject Classification: Primary: 65K05, 65K10; Secondary: 49J52.
Citation: Yazheng Dang, Jie Sun, Honglei Xu. Inertial accelerated algorithms for solving a split feasibility problem. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1383-1394. doi: 10.3934/jimo.2016078
References:
[1]

F. Alvarez, On the minimizing property of a second order dissipative dynamical system in Hilbert spaces, SIAM Journal on Control and Optimization, 39 (2000), 1102-1119.  doi: 10.1137/S0363012998335802.  Google Scholar

[2]

F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via Discretization of a nonlinear oscillator with damping, Set-Valued Analysis, 9 (2001), 3-11.  doi: 10.1023/A:1011253113155.  Google Scholar

[3]

F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space, SIAM Journal on Optimization, 14 (2003), 773-782.  doi: 10.1137/S1052623403427859.  Google Scholar

[4]

H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Review, 38 (1996), 367-426.  doi: 10.1137/S0036144593251710.  Google Scholar

[5]

C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453.  doi: 10.1088/0266-5611/18/2/310.  Google Scholar

[6]

C. Byrne, An unified treatment of some iterative algorithm algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120.  doi: 10.1088/0266-5611/20/1/006.  Google Scholar

[7]

J. W. Chinneck, The constraint consensus method for finding approximately feasible points in nonlinear programs, INFORMS Journal on Computing, 16 (2004), 255-265.  doi: 10.1287/ijoc.1030.0046.  Google Scholar

[8]

Y. Censor, Parallel application of block iterative methods in medical imaging and radiation therapy, Mathematical Programming, 42 (1998), 307-325.  doi: 10.1007/BF01589408.  Google Scholar

[9]

Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, 8 (1994), 221-239.  doi: 10.1007/BF02142692.  Google Scholar

[10]

Y. Censor, T. Elfving, N. Kopf and T. Bortfeld, The multiple-sets solit feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084.  doi: 10.1088/0266-5611/21/6/017.  Google Scholar

[11]

G. Crombez, A geometrical look at iterative methods for operators with fixed points, Numerical Functional Analysis and Optimization, 26 (2005), 137-175.  doi: 10.1081/NFA-200063882.  Google Scholar

[12]

F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983.  Google Scholar

[13]

F. Deutsch, The method of alternating orthogonal projections, Approximation Theory, Spline Functions and Applications, 105-121, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , 356, Kluwer Acad. Publ. , Dordrecht, 1992 Google Scholar

[14]

Y. Dang and Y. Gao, The strong convergence of a KM-CQ-Like algorithm for split feasibility problem, Inverse Problems 27 (2011), 015007, 9 pp. doi: 10.1088/0266-5611/27/1/015007.  Google Scholar

[15]

M. Fukushima, On the convergence of a class of outer approximation algorithms for convex programs, Journal of Computational and Applied Mathematics, 10 (1984), 147-156.  doi: 10.1016/0377-0427(84)90051-7.  Google Scholar

[16]

M. Fukushima, A relaxed projection method for variational inequalities, Mathematics Programming, 35 (1986), 58-70.  doi: 10.1007/BF01589441.  Google Scholar

[17]

Y. Gao, Piecewise smooth Lyapunov function for a nonlinear dynamical system, Journal of Convex Analysis, 19 (2012), 1009-1015.   Google Scholar

[18]

G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography, Academic Press, New York, 1980.  Google Scholar

[19]

P. E. Mainge, Inertial iterative process for fixed points of certain quasi-nonexpansive mappings, Set-valued Analysis, 15 (2007), 67-79.  doi: 10.1007/s11228-006-0027-3.  Google Scholar

[20]

P. E. Mainge, Convergence theorem for inertial KM-type algorithms, Journal of Computational and Applied Mathematics, 219 (2008), 223-236.  doi: 10.1016/j.cam.2007.07.021.  Google Scholar

[21]

Z. Opial, Weak convergence of the sequence of successive approximations for non-expansive mappings, Bull. American Mathematical Society, 73 (1967), 591-597.  doi: 10.1090/S0002-9904-1967-11761-0.  Google Scholar

[22]

B. Qu and N. Xiu, A new halfspace-relaxation projection method for the split feasibility problem, Linear Algebra and Its Application, 428 (2008), 1218-1229.  doi: 10.1016/j.laa.2007.03.002.  Google Scholar

[23]

H. Xu, A variabe Krasnoselski-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034.  doi: 10.1088/0266-5611/22/6/007.  Google Scholar

[24]

Q. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266.  doi: 10.1088/0266-5611/20/4/014.  Google Scholar

[25]

A. L. Yan, G. Y. Wang and N. H. Xiu, Robust solutions of split feasibility problem with uncertain linear operator, Journal of Industrial and Management Optimization, 3 (2007), 749-761.  doi: 10.3934/jimo.2007.3.749.  Google Scholar

[26]

J. Zhao and Q. Yang, Several solution methods for the split feasibility problem, Inverse Problems, 21 (2005), 1791-1799.  doi: 10.1088/0266-5611/21/5/017.  Google Scholar

show all references

References:
[1]

F. Alvarez, On the minimizing property of a second order dissipative dynamical system in Hilbert spaces, SIAM Journal on Control and Optimization, 39 (2000), 1102-1119.  doi: 10.1137/S0363012998335802.  Google Scholar

[2]

F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via Discretization of a nonlinear oscillator with damping, Set-Valued Analysis, 9 (2001), 3-11.  doi: 10.1023/A:1011253113155.  Google Scholar

[3]

F. Alvarez, Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space, SIAM Journal on Optimization, 14 (2003), 773-782.  doi: 10.1137/S1052623403427859.  Google Scholar

[4]

H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Review, 38 (1996), 367-426.  doi: 10.1137/S0036144593251710.  Google Scholar

[5]

C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453.  doi: 10.1088/0266-5611/18/2/310.  Google Scholar

[6]

C. Byrne, An unified treatment of some iterative algorithm algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120.  doi: 10.1088/0266-5611/20/1/006.  Google Scholar

[7]

J. W. Chinneck, The constraint consensus method for finding approximately feasible points in nonlinear programs, INFORMS Journal on Computing, 16 (2004), 255-265.  doi: 10.1287/ijoc.1030.0046.  Google Scholar

[8]

Y. Censor, Parallel application of block iterative methods in medical imaging and radiation therapy, Mathematical Programming, 42 (1998), 307-325.  doi: 10.1007/BF01589408.  Google Scholar

[9]

Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, 8 (1994), 221-239.  doi: 10.1007/BF02142692.  Google Scholar

[10]

Y. Censor, T. Elfving, N. Kopf and T. Bortfeld, The multiple-sets solit feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084.  doi: 10.1088/0266-5611/21/6/017.  Google Scholar

[11]

G. Crombez, A geometrical look at iterative methods for operators with fixed points, Numerical Functional Analysis and Optimization, 26 (2005), 137-175.  doi: 10.1081/NFA-200063882.  Google Scholar

[12]

F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983.  Google Scholar

[13]

F. Deutsch, The method of alternating orthogonal projections, Approximation Theory, Spline Functions and Applications, 105-121, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , 356, Kluwer Acad. Publ. , Dordrecht, 1992 Google Scholar

[14]

Y. Dang and Y. Gao, The strong convergence of a KM-CQ-Like algorithm for split feasibility problem, Inverse Problems 27 (2011), 015007, 9 pp. doi: 10.1088/0266-5611/27/1/015007.  Google Scholar

[15]

M. Fukushima, On the convergence of a class of outer approximation algorithms for convex programs, Journal of Computational and Applied Mathematics, 10 (1984), 147-156.  doi: 10.1016/0377-0427(84)90051-7.  Google Scholar

[16]

M. Fukushima, A relaxed projection method for variational inequalities, Mathematics Programming, 35 (1986), 58-70.  doi: 10.1007/BF01589441.  Google Scholar

[17]

Y. Gao, Piecewise smooth Lyapunov function for a nonlinear dynamical system, Journal of Convex Analysis, 19 (2012), 1009-1015.   Google Scholar

[18]

G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography, Academic Press, New York, 1980.  Google Scholar

[19]

P. E. Mainge, Inertial iterative process for fixed points of certain quasi-nonexpansive mappings, Set-valued Analysis, 15 (2007), 67-79.  doi: 10.1007/s11228-006-0027-3.  Google Scholar

[20]

P. E. Mainge, Convergence theorem for inertial KM-type algorithms, Journal of Computational and Applied Mathematics, 219 (2008), 223-236.  doi: 10.1016/j.cam.2007.07.021.  Google Scholar

[21]

Z. Opial, Weak convergence of the sequence of successive approximations for non-expansive mappings, Bull. American Mathematical Society, 73 (1967), 591-597.  doi: 10.1090/S0002-9904-1967-11761-0.  Google Scholar

[22]

B. Qu and N. Xiu, A new halfspace-relaxation projection method for the split feasibility problem, Linear Algebra and Its Application, 428 (2008), 1218-1229.  doi: 10.1016/j.laa.2007.03.002.  Google Scholar

[23]

H. Xu, A variabe Krasnoselski-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems, 22 (2006), 2021-2034.  doi: 10.1088/0266-5611/22/6/007.  Google Scholar

[24]

Q. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266.  doi: 10.1088/0266-5611/20/4/014.  Google Scholar

[25]

A. L. Yan, G. Y. Wang and N. H. Xiu, Robust solutions of split feasibility problem with uncertain linear operator, Journal of Industrial and Management Optimization, 3 (2007), 749-761.  doi: 10.3934/jimo.2007.3.749.  Google Scholar

[26]

J. Zhao and Q. Yang, Several solution methods for the split feasibility problem, Inverse Problems, 21 (2005), 1791-1799.  doi: 10.1088/0266-5611/21/5/017.  Google Scholar

Table 1.  The numerical results of example 5.1
Initiative pointR-IterIner-R-Iter
$ x^{0}=(3.2, 4.2, 5.2)$ $ k=74; s =0.068$$ k=5; s=0.016$
$ x^{1}=(-0.5843, $ $x^{\ast}=(-0.6200, 1.6180, 1.6216)$ $x^{\ast}=(-1.1281, 1.0720, 1.9694)$
$2.3078, 3.3435) $
$ x^{0}=(10, 0, 10)$$ k=93; s =0.090$$ k=84; s=0.085$
$ x^{1}=(2.0825, $ $x^{\ast}=(0.9000, -1.7152, 1.7074)$ $x^{\ast}=(-0.1061, -1.4514, 2.1596)$
$-2.5275, 6.4589) $
$ x^{0}=(2, -5, 2)$$ k=73; s =0.075$$ k=35; s =0.035$
$x^{1}=(1.3327, $ $x^{\ast}=(1.1512, -2.7679;1.8616)$ $x^{\ast}=(0.9010, -2.1029, 1.8169)$
$-3.2657, 1.9328) $
Table Options

Download as excel

Initiative pointR-IterIner-R-Iter
$ x^{0}=(3.2, 4.2, 5.2)$ $ k=74; s =0.068$$ k=5; s=0.016$
$ x^{1}=(-0.5843, $ $x^{\ast}=(-0.6200, 1.6180, 1.6216)$ $x^{\ast}=(-1.1281, 1.0720, 1.9694)$
$2.3078, 3.3435) $
$ x^{0}=(10, 0, 10)$$ k=93; s =0.090$$ k=84; s=0.085$
$ x^{1}=(2.0825, $ $x^{\ast}=(0.9000, -1.7152, 1.7074)$ $x^{\ast}=(-0.1061, -1.4514, 2.1596)$
$-2.5275, 6.4589) $
$ x^{0}=(2, -5, 2)$$ k=73; s =0.075$$ k=35; s =0.035$
$x^{1}=(1.3327, $ $x^{\ast}=(1.1512, -2.7679;1.8616)$ $x^{\ast}=(0.9010, -2.1029, 1.8169)$
$-3.2657, 1.9328) $
Table 2.  The numerical results of example 5.1
Initiative point$\alpha_{k}$Iner-KM-R-Iter
$ x^{0}=(3.2, 4.2, 5.2)$0.4$ k=3; s=0.016$
$ x^{1}=(-0.5843, 2.3078, 3.3435)$ $x^{\ast}=(-2.6931, 1.2534, 2.2937)$
0.8 $k=3; s= 0.013$
$x^{\ast}=(-2.6828, 1.2585, 2.2835)$
$ x^{0}=(10, 0, 10)$0.4$ k=76; s =0.086$
$ x^{1}=(2.0825, -2.5275, 6.4589)$ $x^{\ast}=(-0.1346, -2.6392, 2.3046)$
0.8 $ k= 74; s=0.085 $
$x^{\ast}=(-0.0799, -2.6190, 2.3611)$
$ x^{0}=(2, -5, 2)$0.6$ k=62; s =0.056$
$ x^{1}=(1.3327, -3.2657, 1.9328)$ $x^{\ast}=(0.9006, -2.1031, 1.8171)$
0.8 $ k=45; s= 0.046$
$x^{\ast}=(0.9008, -2.1030, 1.8170)$
Table Options

Download as excel

Initiative point$\alpha_{k}$Iner-KM-R-Iter
$ x^{0}=(3.2, 4.2, 5.2)$0.4$ k=3; s=0.016$
$ x^{1}=(-0.5843, 2.3078, 3.3435)$ $x^{\ast}=(-2.6931, 1.2534, 2.2937)$
0.8 $k=3; s= 0.013$
$x^{\ast}=(-2.6828, 1.2585, 2.2835)$
$ x^{0}=(10, 0, 10)$0.4$ k=76; s =0.086$
$ x^{1}=(2.0825, -2.5275, 6.4589)$ $x^{\ast}=(-0.1346, -2.6392, 2.3046)$
0.8 $ k= 74; s=0.085 $
$x^{\ast}=(-0.0799, -2.6190, 2.3611)$
$ x^{0}=(2, -5, 2)$0.6$ k=62; s =0.056$
$ x^{1}=(1.3327, -3.2657, 1.9328)$ $x^{\ast}=(0.9006, -2.1031, 1.8171)$
0.8 $ k=45; s= 0.046$
$x^{\ast}=(0.9008, -2.1030, 1.8170)$
Table 3.  The numerical results of example 5.2
Initiative pointR-IterIner-R-Iter
$ x^{0}=(0, 0, 0, 0, 0)$$ k=15$; s $=0.675$$ k=5$; s $=0.018$
$ x^{1}=(-0.0092, 0, $ $x^{\ast}=(-0.0208, 0, $ $x^{\ast}=(0.0015, 0, $
$-0.0132, -0.0026, -0.0092)$ $-0.0297, -0.0059, -0.0208) $ $-0.0412, -0.0082, -0.0288) $
$ x^{0}=(1, 1, 1, 1, 1)$$ k=20$; s $=0.083$$ k=3$; s $=0.0272$
$ x^{1}=(0.3237, 0.5471, $ $x^{\ast}=(0.0171, 0.3822, $ $x^{\ast}=(-0.0784, 0.2935, $
$ 0.2280, 0.4833, 0.3237) $ $ -0.1394, 0.2779, 0.0171) $ $ -0.2378, 0.1873, -0.0784) $
$ x^{0}=(20, 10, 20, 10, 20)$$ k=22$; s $=0.090$$ k=6$; s $=0.067$
$x^{1}=(6.1605, 5.0023, $ $x^{\ast}=(0.0837, 0.3910, $ $x^{\ast}=(-0.2490, -0.2117, $
$4.5130, 3.9040, 6.1605)$ $ -0.2155, 0.1915, 0.0837) $ $ -0.1742, -0.1619, -0.2490) $
Table Options

Download as excel

Initiative pointR-IterIner-R-Iter
$ x^{0}=(0, 0, 0, 0, 0)$$ k=15$; s $=0.675$$ k=5$; s $=0.018$
$ x^{1}=(-0.0092, 0, $ $x^{\ast}=(-0.0208, 0, $ $x^{\ast}=(0.0015, 0, $
$-0.0132, -0.0026, -0.0092)$ $-0.0297, -0.0059, -0.0208) $ $-0.0412, -0.0082, -0.0288) $
$ x^{0}=(1, 1, 1, 1, 1)$$ k=20$; s $=0.083$$ k=3$; s $=0.0272$
$ x^{1}=(0.3237, 0.5471, $ $x^{\ast}=(0.0171, 0.3822, $ $x^{\ast}=(-0.0784, 0.2935, $
$ 0.2280, 0.4833, 0.3237) $ $ -0.1394, 0.2779, 0.0171) $ $ -0.2378, 0.1873, -0.0784) $
$ x^{0}=(20, 10, 20, 10, 20)$$ k=22$; s $=0.090$$ k=6$; s $=0.067$
$x^{1}=(6.1605, 5.0023, $ $x^{\ast}=(0.0837, 0.3910, $ $x^{\ast}=(-0.2490, -0.2117, $
$4.5130, 3.9040, 6.1605)$ $ -0.2155, 0.1915, 0.0837) $ $ -0.1742, -0.1619, -0.2490) $
Table 4.  The numerical results of example 5.2
Initiative point$\alpha_{k}$Iner-KM-R-Iter
$ x^{0}=(0, 0, 0, 0, 0)$0.6$ k=6$; s $=0.020$
$ x^{1}=(-0.0092, 0, -0.0132, $ $x^{\ast}=(-0.0209, 0, -0.0299, -0.0059, -0.0209)$
$-0.0026, -0.0092) $0.8k=5; s=0.018
$x^{\ast}=(-0.0212, 0, -0.0304, -0.0060, -0.0212)$
$ x^{0}=(1, 1, 1, 1, 1)$0.4$ k=3$; s $=0.034$
$ x^{1}=(0.3237, 0.5471, $ $x^{\ast}=(-0.0644, 0.2935, -0.2177, 0.1913, -0.0644)$
$ 0.2280, 0.4833, 0.3237) $0.6k=3; s=0.034
$x^{\ast}=(-0.0691, 0.2935, -0.2244, 0.1899, -0.0691) $
$ x^{0}=(20, 10, 20, 10, 20)$0.6$ k=9$; s $=0.072$
$ x^{1}=(6.1605, 5.0023, $ $x^{\ast}=(-0.2263, -0.1045, -0.2337, -0.1094, -0.2263)$
$4.5130, 3.9040, 6.1605) $0.8k= 7; s=0.071
$x^{\ast}=(-0.2283, -0.1610, -0.1881, -0.1342, -0.2283)$
Table Options

Download as excel

Initiative point$\alpha_{k}$Iner-KM-R-Iter
$ x^{0}=(0, 0, 0, 0, 0)$0.6$ k=6$; s $=0.020$
$ x^{1}=(-0.0092, 0, -0.0132, $ $x^{\ast}=(-0.0209, 0, -0.0299, -0.0059, -0.0209)$
$-0.0026, -0.0092) $0.8k=5; s=0.018
$x^{\ast}=(-0.0212, 0, -0.0304, -0.0060, -0.0212)$
$ x^{0}=(1, 1, 1, 1, 1)$0.4$ k=3$; s $=0.034$
$ x^{1}=(0.3237, 0.5471, $ $x^{\ast}=(-0.0644, 0.2935, -0.2177, 0.1913, -0.0644)$
$ 0.2280, 0.4833, 0.3237) $0.6k=3; s=0.034
$x^{\ast}=(-0.0691, 0.2935, -0.2244, 0.1899, -0.0691) $
$ x^{0}=(20, 10, 20, 10, 20)$0.6$ k=9$; s $=0.072$
$ x^{1}=(6.1605, 5.0023, $ $x^{\ast}=(-0.2263, -0.1045, -0.2337, -0.1094, -0.2263)$
$4.5130, 3.9040, 6.1605) $0.8k= 7; s=0.071
$x^{\ast}=(-0.2283, -0.1610, -0.1881, -0.1342, -0.2283)$
Table 5.  The numerical results of example 5.3
$M, N $R-IterIner-R-IterIner-KM-R-Iter
$ M=20, N=10$$ k=436, s =0.970$$ k=174, s =0.500$ $ k=210, s =0.270$
$M=100, N=90$$ k=3788, s =0.130$$ k=602, s =0.680$ $ k=534, s =0.690$
Table Options

Download as excel

$M, N $R-IterIner-R-IterIner-KM-R-Iter
$ M=20, N=10$$ k=436, s =0.970$$ k=174, s =0.500$ $ k=210, s =0.270$
$M=100, N=90$$ k=3788, s =0.130$$ k=602, s =0.680$ $ k=534, s =0.690$
[1]

Guash Haile Taddele, Poom Kumam, Habib ur Rehman, Anteneh Getachew Gebrie. Self adaptive inertial relaxed $ CQ $ algorithms for solving split feasibility problem with multiple output sets. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021172
[2]

Suthep Suantai, Nattawut Pholasa, Prasit Cholamjiak. The modified inertial relaxed CQ algorithm for solving the split feasibility problems. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1595-1615. doi: 10.3934/jimo.2018023
[3]

Ai-Ling Yan, Gao-Yang Wang, Naihua Xiu. Robust solutions of split feasibility problem with uncertain linear operator. Journal of Industrial & Management Optimization, 2007, 3 (4) : 749-761. doi: 10.3934/jimo.2007.3.749
[4]

Zeng-Zhen Tan, Rong Hu, Ming Zhu, Ya-Ping Fang. A dynamical system method for solving the split convex feasibility problem. Journal of Industrial & Management Optimization, 2021, 17 (6) : 2989-3011. doi: 10.3934/jimo.2020104
[5]

Yazheng Dang, Fanwen Meng, Jie Sun. Convergence analysis of a parallel projection algorithm for solving convex feasibility problems. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 505-519. doi: 10.3934/naco.2016023
[6]

Ya-Zheng Dang, Zhong-Hui Xue, Yan Gao, Jun-Xiang Li. Fast self-adaptive regularization iterative algorithm for solving split feasibility problem. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1555-1569. doi: 10.3934/jimo.2019017
[7]

Yan Tang. Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. Journal of Industrial & Management Optimization, 2020, 16 (2) : 945-964. doi: 10.3934/jimo.2018187
[8]

Ya-zheng Dang, Jie Sun, Su Zhang. Double projection algorithms for solving the split feasibility problems. Journal of Industrial & Management Optimization, 2019, 15 (4) : 2023-2034. doi: 10.3934/jimo.2018135
[9]

Xueling Zhou, Meixia Li, Haitao Che. Relaxed successive projection algorithm with strong convergence for the multiple-sets split equality problem. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2557-2572. doi: 10.3934/jimo.2020082
[10]

Sanming Liu, Zhijie Wang, Chongyang Liu. On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 389-402. doi: 10.3934/jimo.2016.12.389
[11]

Preeyanuch Chuasuk, Ferdinard Ogbuisi, Yekini Shehu, Prasit Cholamjiak. New inertial method for generalized split variational inclusion problems. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3357-3371. doi: 10.3934/jimo.2020123
[12]

Chibueze Christian Okeke, Abdulmalik Usman Bello, Lateef Olakunle Jolaoso, Kingsley Chimuanya Ukandu. Inertial method for split null point problems with pseudomonotone variational inequality problems. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021037
[13]

Aviv Gibali, Dang Thi Mai, Nguyen The Vinh. A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. Journal of Industrial & Management Optimization, 2019, 15 (2) : 963-984. doi: 10.3934/jimo.2018080
[14]

Vladimir F. Demyanov, Julia A. Ryabova. Exhausters, coexhausters and converters in nonsmooth analysis. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1273-1292. doi: 10.3934/dcds.2011.31.1273
[15]

Timilehin Opeyemi Alakoya, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo. A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020152
[16]

George W. Patrick. The geometry of convergence in numerical analysis. Journal of Computational Dynamics, 2021, 8 (1) : 33-58. doi: 10.3934/jcd.2021003
[17]

Jamilu Abubakar, Poom Kumam, Abor Isa Garba, Muhammad Sirajo Abdullahi, Abdulkarim Hassan Ibrahim, Wachirapong Jirakitpuwapat. An efficient iterative method for solving split variational inclusion problem with applications. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021160
[18]

Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial & Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485
[19]

David Bourne, Howard Elman, John E. Osborn. A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part II: Analysis of Convergence. Communications on Pure & Applied Analysis, 2009, 8 (1) : 143-160. doi: 10.3934/cpaa.2009.8.143
[20]

Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (189)
  • HTML views (394)
  • Cited by (16)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences