scholarly journals The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates

2020 ◽  
Vol 45 (2) ◽  
pp. 682-712
Author(s):  
Radu Ioan Boţ ◽  
Dang-Khoa Nguyen
Keyword(s):  
Convergence Analysis ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Proximal Alternating Direction Method

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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