October  2007, 3(4): 749-761. doi: 10.3934/jimo.2007.3.749

Robust solutions of split feasibility problem with uncertain linear operator

1. 

Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P.R., China, China

2. 

Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R.

Received  November 2006 Revised  January 2007 Published  October 2007

In this paper, we treat the split feasibility problem with uncertain linear operator (USFP). For this problem, we first reformulate it as an uncertain optimization problem (UOP) with zero optimal value, and then we introduce robust counterparts of the UOP and reformulate them as the tractable convex optimization problems. These convex optimization problems have close connection with the robust counterparts of USFP and the minimum SFPs under the appropriate conditions. In the end of this paper, we give some numerical results to illustrate the effectiveness of the robust solutions of the concerned problem.
Citation: 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
[1]

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

[2]

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

[3]

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

[4]

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

[5]

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

[6]

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

[7]

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

[8]

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

[9]

Grace Nnennaya Ogwo, Chinedu Izuchukwu, Oluwatosin Temitope Mewomo. A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021011

[10]

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

[11]

Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021046

[12]

Angelot Behajaina. On BCH split metacyclic codes. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021045

[13]

Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227

[14]

Liqun Qi, Zheng yan, Hongxia Yin. Semismooth reformulation and Newton's method for the security region problem of power systems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 143-153. doi: 10.3934/jimo.2008.4.143

[15]

Yi Jiang, Yuan Cai. A reformulation-linearization based algorithm for the smallest enclosing circle problem. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3633-3644. doi: 10.3934/jimo.2020136

[16]

Monica Motta. Minimum time problem with impulsive and ordinary controls. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5781-5809. doi: 10.3934/dcds.2018252

[17]

David Ginzburg. Constructing automorphic representations in split classical groups. Electronic Research Announcements, 2012, 19: 18-32. doi: 10.3934/era.2012.19.18

[18]

Dang Van Hieu. Projection methods for solving split equilibrium problems. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2331-2349. doi: 10.3934/jimo.2019056

[19]

Litao Guo, Bernard L. S. Lin. Vulnerability of super connected split graphs and bisplit graphs. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1179-1185. doi: 10.3934/dcdss.2019081

[20]

Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (58)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]