Proximal bundle methods for nonsmooth DC programming

2019 ◽  
Vol 75 (2) ◽  
pp. 523-563 ◽  
Author(s):  
Welington de Oliveira
Keyword(s):  
Dc Programming ◽  
Bundle Methods ◽  
Proximal Bundle Methods

Convex proximal bundle methods in depth: a unified analysis for inexact oracles

2014 ◽  
Vol 148 (1-2) ◽  
pp. 241-277 ◽  
Author(s):  
W. de Oliveira ◽  
C. Sagastizábal ◽  
C. Lemaréchal
Keyword(s):  
Bundle Methods ◽  
Proximal Bundle Methods

Alternating DC algorithm for partial DC programming problems

2021 ◽  
Author(s):  
Tao Pham Dinh ◽  
Van Ngai Huynh ◽  
Hoai An Le Thi ◽  
Vinh Thanh Ho
Keyword(s):  
Dc Programming ◽  
Dc Algorithm

scholarly journals An Efficient Method for Convex Constrained Rank Minimization Problems Based on DC Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wanping Yang ◽  
Jinkai Zhao ◽  
Fengmin Xu
Keyword(s):  
Objective Function ◽  
Minimization Problem ◽  
Dc Programming ◽  
Rank Minimization ◽  
Closed Form Solutions ◽  
Minimization Problems ◽  
Difference Of Convex Functions ◽  
Convex Objective Function ◽  
Difference Of Convex ◽  
Cut Problems

The constrained rank minimization problem has various applications in many fields including machine learning, control, and signal processing. In this paper, we consider the convex constrained rank minimization problem. By introducing a new variable and penalizing an equality constraint to objective function, we reformulate the convex objective function with a rank constraint as a difference of convex functions based on the closed-form solutions, which can be reformulated as DC programming. A stepwise linear approximative algorithm is provided for solving the reformulated model. The performance of our method is tested by applying it to affine rank minimization problems and max-cut problems. Numerical results demonstrate that the method is effective and of high recoverability and results on max-cut show that the method is feasible, which provides better lower bounds and lower rank solutions compared with improved approximation algorithm using semidefinite programming, and they are close to the results of the latest researches.

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