Primal-dual proximal point algorithm for linearly constrained convex programming problems

1992 ◽  
Vol 1 (2) ◽  
pp. 207-226 ◽  
Author(s):  
Satoru Ibaraki ◽  
Masao Fukushima ◽  
Toshihide Ibaraki
Keyword(s):  
Convex Programming ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Linearly Constrained Convex Programming ◽  
Primal Dual ◽  
Linearly Constrained

scholarly journals A General Self-Adaptive Relaxed-PPA Method for Convex Programming with Linear Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaoling Fu
Keyword(s):  
Convex Programming ◽  
State Of The Art ◽  
Adaptive Strategies ◽  
Linear Constraints ◽  
Proximal Point ◽  
Mild Conditions ◽  
Linearly Constrained Convex Programming ◽  
Linearly Constrained ◽  
Algorithmic Framework ◽  
Self Adaptive

We present an efficient method for solving linearly constrained convex programming. Our algorithmic framework employs an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA). In particular, the stepsize choice condition of our algorithm is weaker than some elegant PPA-type methods. This condition is flexible and effective. Self-adaptive strategies are proposed to improve the convergence in practice. We theoretically show under mild conditions that our method converges in a global sense. Finally, we discuss applications and perform numerical experiments which confirm the efficiency of the proposed method. Comparisons of our method with some state-of-the-art algorithms are also provided.

scholarly journals Convergence Analysis on an Accelerated Proximal Point Algorithm for Linearly Constrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Sha Lu ◽  
Zengxin Wei
Keyword(s):  
Machine Learning ◽  
Linear Programming ◽  
Proximal Point Algorithm ◽  
Original Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Proximal Point ◽  
Constrained Optimization Problems ◽  
Linearly Constrained ◽  
Linear Programming Problems

Proximal point algorithm is a type of method widely used in solving optimization problems and some practical problems such as machine learning in recent years. In this paper, a framework of accelerated proximal point algorithm is presented for convex minimization with linear constraints. The algorithm can be seen as an extension to G u ¨ ler’s methods for unconstrained optimization and linear programming problems. We prove that the sequence generated by the algorithm converges to a KKT solution of the original problem under appropriate conditions with the convergence rate of O 1 / k 2 .

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