Complexity analysis of a full-Newton step interior-point method for linear optimization

2016 ◽  
Vol 73 (1) ◽  
pp. 27-42 ◽  
Author(s):  
Zsolt Darvay ◽  
Ingrid-Magdolna Papp ◽  
Petra-Renáta Takács
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Linear Optimization ◽  
Point Method ◽  
Newton Step ◽  
Full Newton Step

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION BASED ON AN EXPONENTIAL KERNEL FUNCTION

2014 ◽  
Vol 07 (01) ◽  
pp. 1450018
Author(s):  
Behrouz Kheirfam ◽  
Fariba Hasani
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Polynomial Complexity ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Math Model ◽  
Newton Step ◽  
Infeasible Interior Point Method ◽  
Full Newton Step

This paper deals with an infeasible interior-point algorithm with full-Newton step for linear optimization based on a kernel function, which is an extension of the work of the first author and coworkers (J. Math. Model Algorithms (2013); DOI 10.1007/s10852-013-9227-7). The main iteration of the algorithm consists of a feasibility step and several centrality steps. The centrality step is based on Darvay's direction, while we used a kernel function in the algorithm to induce the feasibility step. For the kernel function, the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods.

A Full-Newton Step Interior-point Method Based on a Class of Specific Algebra Transformation

2018 ◽  
Vol 163 (4) ◽  
pp. 325-337 ◽  
Author(s):  
Behrouz Kheirfam ◽  
Afsaneh Nasrollahi
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Newton Step ◽  
Full Newton Step
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