An infeasible interior-point algorithm with full-Newton step for linear optimization

2007 ◽  
Vol 46 (2) ◽  
pp. 173-188 ◽  
Author(s):  
Zhongyi Liu ◽  
Wenyu Sun
Keyword(s):  
Interior Point ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
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 polynomial-time weighted path-following interior-point algorithm for linear optimization

2018 ◽  
Vol 13 (02) ◽  
pp. 2050038
Author(s):  
Mohamed Achache
Keyword(s):  
Polynomial Time ◽  
Interior Point ◽  
Line Search ◽  
Linear Optimization ◽  
Path Following ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Iteration Bound ◽  
Primal Dual ◽  
Full Newton Step

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an [Formula: see text]-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, [Formula: see text]. This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.

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.

A MODIFIED FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR LINEAR OPTIMIZATION

2013 ◽  
Vol 30 (06) ◽  
pp. 1350027 ◽  
Author(s):  
B. KHEIRFAM ◽  
K. AHMADI ◽  
F. HASANI
Keyword(s):  
Interior Point ◽  
Time Complexity ◽  
Dual Problem ◽  
Numerical Study ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Numerical Performance ◽  
The Given ◽  
Full Newton Step

We present a full-Newton step infeasible interior-point algorithm based on a new search direction. The algorithm decreases the duality gap and the feasibility residuals at the same rate. During this algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the algorithm consists of a feasibility step and some centering steps. We show that the algorithm converges and finds an approximate solution in a polynomial time complexity. A numerical study is done for its numerical performance.

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