scholarly journals PRIMAL-DUAL ALGORITHMS FOR SEMIDEFINIT OPTIMIZATION PROBLEMS BASED ON GENERALIZED TRIGONOMETRIC BARRIER FUNCTION

2017 ◽  
Vol 114 (4) ◽  
Author(s):  
M. El Ghami
Keyword(s):  
Barrier Function ◽  
Optimization Problems ◽  
Primal Dual

Primal–Dual Mirror Descent Method for Constraint Stochastic Optimization Problems

2018 ◽  
Vol 58 (11) ◽  
pp. 1728-1736 ◽  
Author(s):  
A. S. Bayandina ◽  
A. V. Gasnikov ◽  
E. V. Gasnikova ◽  
S. V. Matsievskii
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Descent Method ◽  
Mirror Descent Method ◽  
Mirror Descent ◽  
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.

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