A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion

2013 ◽  
Vol 6 (3) ◽  
pp. 1758-1789 ◽  
Author(s):  
Yangyang Xu ◽  
Wotao Yin
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Block Coordinate Descent ◽  
Tensor Factorization ◽  
Nonnegative Tensor ◽  
Coordinate Descent Method ◽  
Nonnegative Tensor Factorization ◽  
Block Coordinate Descent Method

scholarly journals A block coordinate descent method for sensor network localization

2021 ◽  
Author(s):  
Mitsuhiro Nishijima ◽  
Kazuhide Nakata
Keyword(s):  
Objective Function ◽  
Sensor Network ◽  
Descent Method ◽  
Coordinate Descent ◽  
Block Coordinate Descent ◽  
Penalty Parameter ◽  
Coordinate Descent Method ◽  
Network Localization ◽  
Block Coordinate Descent Method ◽  
Rank Constraint

AbstractThe problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank constraint into a product of two matrices via the Burer–Monteiro factorization. Then, we add the difference of the two matrices, with a penalty parameter, to the objective function, thereby reformulating SNL as an unconstrained multiconvex optimization problem, to which we apply the block coordinate descent method. In this paper, we also provide theoretical analyses of the proposed method and show that each subproblem that is solved sequentially by the block coordinate descent method can also be solved analytically, with the sequence generated by our proposed algorithm converging to a stationary point of the objective function. We also give a range of the penalty parameter for which the two matrices used in the factorization agree at any accumulation point. Numerical experiments confirm that the proposed method does inherit the rank constraint and that it estimates sensor positions faster than other methods without sacrificing the estimation accuracy, especially when the measured distances contain errors.

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