scholarly journals A proximal alternating direction method for $\ell_{2,1}$-norm least squares problem in multi-task feature learning

2012 ◽  
Vol 8 (4) ◽  
pp. 1057-1069 ◽  
Author(s):  
Yunhai Xiao ◽  
◽  
Soon-Yi Wu ◽  
Bing-Sheng He ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Feature Learning ◽  
Alternating Direction Method ◽  
Least Squares Problem ◽  
Alternating Direction ◽  
Task Feature ◽  
Proximal Alternating Direction Method

scholarly journals Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem

2012 ◽  
Vol 2 (4) ◽  
pp. 326-341 ◽  
Author(s):  
Raymond H. Chan ◽  
Min Tao ◽  
Xiaoming Yuan
Keyword(s):  
Least Squares ◽  
Closed Form Solution ◽  
Form Solution ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Linear Least Squares ◽  
Least Squares Problem ◽  
Alternating Direction ◽  
Linear Least Squares Problem ◽  
Speed Up

Abstract.The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.

scholarly journals The PPADMM Method for Solving Quadratic Programming Problems

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 941
Author(s):  
Hai-Long Shen ◽  
Xu Tang
Keyword(s):  
Quadratic Programming ◽  
Alternating Direction Method ◽  
Equality Constraint ◽  
Matrix Analysis ◽  
Method Of Multipliers ◽  
Numerical Examples ◽  
Alternating Direction ◽  
Quadratic Programming Problems ◽  
Proximal Alternating Direction Method

In this paper, a preconditioned and proximal alternating direction method of multipliers (PPADMM) is established for iteratively solving the equality-constraint quadratic programming problems. Based on strictly matrix analysis, we prove that this method is asymptotically convergent. We also show the connection between this method with some existing methods, so it combines the advantages of the methods. Finally, the numerical examples show that the algorithm proposed is efficient, stable, and flexible for solving the quadratic programming problems with equality constraint.

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