scholarly journals Interior-point methods for second-order cone optimization based on the generalized trigonometric barrier function

2019 ◽  
Vol 1324 ◽  
pp. 012031
Author(s):  
Pengyang Xie ◽  
Jinwei Su ◽  
Xinyin Peng
Keyword(s):  
Interior Point ◽  
Barrier Function ◽  
Interior Point Methods ◽  
Second Order ◽  
Second Order Cone

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.

scholarly journals A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint

2021 ◽  
pp. 427-433
Author(s):  
Mansour Saraj ◽  
Ali Sadeghi ◽  
Nezam Mahdavi Amiri
Keyword(s):  
Programming Problem ◽  
Interior Point ◽  
Barrier Function ◽  
Fractional Programming ◽  
Second Order ◽  
Fractional Programming Problem ◽  
Newton Step ◽  
Cone Constraint ◽  
Second Order Cone ◽  
Logarithmic Barrier

Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier function related to the feasibility set of the underlying problem.Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach.

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