A Splitting Augmented Lagrangian Method for Low Multilinear-Rank Tensor Recovery

Lei Yang (), Zheng-Hai Huang () and Yu-Fan Li ()
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Lei Yang: Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China
Zheng-Hai Huang: Center for Applied Mathematics of Tianjin University, Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China
Yu-Fan Li: Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 01, 1-25

Abstract: This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low multilinear-rank tensor recovery problem. The variable splitting technique and convex relaxation technique are used to transform this problem into a tractable constrained optimization problem. Considering the favorable structure of the problem, we develop a splitting augmented Lagrangian method (SALM) to solve the resulting problem. The proposed algorithm is easily implemented and its convergence can be proved under some conditions. Some preliminary numerical results on randomly generated and real completion problems show that the proposed algorithm is very effective and robust for tackling the low multilinear-rank tensor completion problem.

Keywords: Multilinear-rank; low multilinear-rank tensor recovery; tensor completion; augmented Lagrangian method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915400084

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