scholarly journals On the chaotic behavior of the primal–dual affine–scaling algorithm for linear optimization

2014 ◽  
Vol 24 (4) ◽  
pp. 043132 ◽  
Author(s):  
H. Bruin ◽  
R. Fokkink ◽  
G. Gu ◽  
C. Roos
Keyword(s):  
Chaotic Behavior ◽  
Linear Optimization ◽  
Affine Scaling ◽  
Affine Scaling Algorithm ◽  
Dual Affine ◽  
Primal Dual

A Primal-dual affine scaling algorithm with necessary centering as a safeguard

Optimization ◽  
1995 ◽  
Vol 35 (4) ◽  
pp. 333-343 ◽  
Author(s):  
Gongyun. Zhao ◽  
Jie. Sun ◽  
Jishan. Zhu
Keyword(s):  
Affine Scaling ◽  
Affine Scaling Algorithm ◽  
Dual Affine ◽  
Primal Dual

scholarly journals On the relationship of interior-point methods

1993 ◽  
Vol 16 (3) ◽  
pp. 565-572
Author(s):  
Ruey-Lin Sheu ◽  
Shu-Cherng Fang
Keyword(s):  
Interior Point ◽  
Barrier Function ◽  
Affine Scaling ◽  
Logarithmic Barrier Function ◽  
Scaling Method ◽  
Dual Affine ◽  
Primal Dual ◽  
Affine Scaling Method ◽  
Relationship Of ◽  
Logarithmic Barrier

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic “paths” that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. We also derive the missing dual information in the primal-affine scaling method and the missing primal information in the dual-affine scaling method. Basically, the missing information has the same form as the solutions generated by the primal-dual method but with different scaling matrices.

Sign in / Sign up

Export Citation Format

Share Document