A full-Newton step infeasible interior-point method for linear optimization based on a trigonometric kernel function

Optimization ◽  
2015 ◽  
Vol 65 (4) ◽  
pp. 841-857 ◽  
Author(s):  
B. Kheirfam ◽  
M. Haghighi
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Newton Step ◽  
Infeasible Interior Point Method ◽  
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.

scholarly journals A Full-Newton step infeasible-interior-point algorithm for P*(k)-horizontal linear complementarity problems

2015 ◽  
Vol 25 (1) ◽  
pp. 57-72 ◽  
Author(s):  
S. Asadi ◽  
H. Mansouri
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Infeasible Interior Point Method ◽  
Full Newton Step

In this paper we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problem (HLCP). This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by suitable perturbation in HLCP problem. Then, we use so-called feasibility steps that serves to generate strictly feasible iterates for the next perturbed problem. After accomplishing a few centering steps for the new perturbed problem, we obtain strictly feasible iterates close enough to the central path of the new perturbed problem. The complexity of the algorithm coincides with the best known iteration complexity for infeasible interior-point methods.

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