Robust solutions of split feasibility problem with uncertain linear operator

Ai-Ling Yan; Gao-Yang Wang; Naihua Xiu

doi:10.3934/jimo.2007.3.749

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2007, Volume 3, Issue 4: 749-761. Doi: 10.3934/jimo.2007.3.749

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Robust solutions of split feasibility problem with uncertain linear operator

1.
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, P.R.
2.
Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R.

Received: November 2006

Revised: January 2007

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35C20, 35P20; Secondary: 93D15.

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