# American Institute of Mathematical Sciences

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
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