scholarly journals The Convergent Generalized Central Paths for Linearly Constrained Convex Programming

2018 ◽  
Vol 28 (2) ◽  
pp. 1183-1204 ◽  
Author(s):  
Xun Qian ◽  
Li-Zhi Liao ◽  
Jie Sun ◽  
Hong Zhu
Keyword(s):  
Convex Programming ◽  
Linearly Constrained Convex Programming ◽  
Central Paths ◽  
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.

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