Superlinear primal-dual affine scaling algorithms for LCP

1995 ◽  
Vol 69 (1-3) ◽  
pp. 311-333 ◽  
Author(s):  
R. D. C. Monteiro ◽  
S. J. Wright
Keyword(s):  
Affine Scaling ◽  
Dual Affine ◽  
Primal Dual ◽  
Scaling Algorithms

Primal-Dual Affine-Scaling Algorithms Fail for Semidefinite Programming

1999 ◽  
Vol 24 (1) ◽  
pp. 149-175 ◽  
Author(s):  
Masakazu Muramatsu ◽  
Robert J. Vanderbei
Keyword(s):  
Semidefinite Programming ◽  
Affine Scaling ◽  
Dual Affine ◽  
Primal Dual ◽  
Scaling Algorithms

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

1997 ◽  
Vol 78 (3) ◽  
pp. 315-345 ◽  
Author(s):  
Benjamin Jansen ◽  
Kees Roos ◽  
Tamás Terlaky ◽  
Akiko Yoshise
Keyword(s):  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
Affine Scaling ◽  
Nonlinear Complementarity ◽  
Dual Affine ◽  
Primal Dual ◽  
Scaling Algorithms

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.

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
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