A large-update primal–dual interior-point algorithm for second-order cone optimization based on a new proximity function

Optimization ◽  
2016 ◽  
Vol 65 (7) ◽  
pp. 1477-1496 ◽  
Author(s):  
S. Fathi-Hafshejani ◽  
H. Mansouri ◽  
M. Reza Peyghami
Keyword(s):  
Interior Point ◽  
Second Order ◽  
Interior Point Algorithm ◽  
Proximity Function ◽  
Second Order Cone ◽  
Primal Dual

scholarly journals New complexity analysis of full Nesterov-Todd step infeasible interior point method for second-order cone optimization

2018 ◽  
Vol 28 (1) ◽  
pp. 21-38
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Complexity Analysis ◽  
Second Order ◽  
Interior Point Algorithm ◽  
Complexity Bound ◽  
Second Order Cone ◽  
Infeasible Interior Point Method ◽  
Barrier Parameter

We present a full Nesterov-Todd (NT) step infeasible interior-point algorithm for second-order cone optimization based on a different way to calculate feasibility direction. In each iteration of the algorithm we use the largest possible barrier parameter value ?. Moreover, each main iteration of the algorithm consists of a feasibility step and a few centering steps. The feasibility step differs from the feasibility step of the other existing methods. We derive the complexity bound which coincides with the best known bound for infeasible interior point methods.

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