scholarly journals Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

2016 ◽  
pp. 391-403 ◽  
Author(s):  
Alexey Chernov ◽  
Pavel Dvurechensky ◽  
Alexander Gasnikov
Keyword(s):  
Gradient Method ◽  
Linear Constraints ◽  
Convex Minimization ◽  
Strongly Convex ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Primal Dual ◽  
Dual Gradient

scholarly journals A primal-dual dynamical approach to structured convex minimization problems

2020 ◽  
Vol 269 (12) ◽  
pp. 10717-10757 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Szilárd Csaba László
Keyword(s):  
Convex Minimization ◽  
Minimization Problems ◽  
Dynamical Approach ◽  
Convex Minimization Problems ◽  
Primal Dual

scholarly journals A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block

2015 ◽  
Vol 32 (04) ◽  
pp. 1550024 ◽  
Author(s):  
Min Li ◽  
Defeng Sun ◽  
Kim-Chuan Toh
Keyword(s):  
Linear Equation ◽  
Step Length ◽  
Convex Minimization ◽  
Linear Operators ◽  
Strongly Convex ◽  
Minimization Problems ◽  
Alternating Direction ◽  
Convex Minimization Problems ◽  
Separable Convex Minimization ◽  
Equation Constraint

In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length [Formula: see text] and the penalty parameter σ ∈ (0, +∞). In particular, if σ > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with [Formula: see text].

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