Linearly Constrained Optimization and Simplex Algorithm

2003 ◽  
pp. 291-306
Author(s):  
J. Frédéric Bonnans ◽  
J. Charles Gilbert ◽  
Claude Lemaréchal ◽  
Claudia A. Sagastizábal
Keyword(s):  
Constrained Optimization ◽  
Simplex Algorithm ◽  
Linearly Constrained Optimization ◽  
Linearly Constrained

Quadratically convergent techniques in linearly constrained optimization

AIChE Journal ◽  
1974 ◽  
Vol 20 (3) ◽  
pp. 555-563
Author(s):  
Gregory J. Husen ◽  
James M. Eakman
Keyword(s):  
Constrained Optimization ◽  
Linearly Constrained Optimization ◽  
Linearly Constrained

Faster convergence of a randomized coordinate descent method for linearly constrained optimization problems

2018 ◽  
Vol 16 (05) ◽  
pp. 741-755 ◽  
Author(s):  
Qin Fang ◽  
Min Xu ◽  
Yiming Ying
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Descent Method ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Coordinate Descent Method ◽  
Linearly Constrained Optimization ◽  
Main Challenge ◽  
Linearly Constrained ◽  
Coupled Constraints

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is that the size of data is very large, which makes usual gradient-based methods infeasible. Recently, Necoara, Nesterov and Glineur [Random block coordinate descent methods for linearly constrained optimization over networks, J. Optim. Theory Appl. 173(1) (2017) 227–254] proposed an efficient randomized coordinate descent method to solve this type of optimization problems and presented an appealing convergence analysis. In this paper, we develop new techniques to analyze the convergence of such algorithms, which are able to greatly improve the results presented in the above. This refined result is achieved by extending Nesterov’s second technique [Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM J. Optim. 22 (2012) 341–362] to the general optimization problems with linearly coupled constraints. A novel technique in our analysis is to establish the basis vectors for the subspace of the linear constraints.

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