A full-Newton step infeasible-interior-point algorithm for linear complementarity problems

2011 ◽  
Vol 12 (1) ◽  
pp. 545-561 ◽  
Author(s):  
H. Mansouri ◽  
M. Zangiabadi ◽  
M. Pirhaji
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Full Newton Step

Path-following interior-point algorithm for monotone linear complementarity problems

2021 ◽  
Author(s):  
Welid Grimes
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Path Following ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Barrier Parameter ◽  
Step Algorithm ◽  
Full Newton Step

This paper presents a path-following full-Newton step interior-point algorithm for solving monotone linear complementarity problems. Under new choices of the defaults of the updating barrier parameter [Formula: see text] and the threshold [Formula: see text] which defines the size of the neighborhood of the central-path, we show that the short-step algorithm has the best-known polynomial complexity, namely, [Formula: see text]. Finally, some numerical results are reported to show the efficiency of our algorithm.

An infeasible interior-point method with improved centering steps for monotone linear complementarity problems

2015 ◽  
Vol 08 (03) ◽  
pp. 1550037 ◽  
Author(s):  
Soodabeh Asadi ◽  
Hossein Mansouri ◽  
Zsolt Darvay
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Nonlinear Anal ◽  
Infeasible Interior Point Method ◽  
Full Newton Step

In this paper, we improve the infeasible full-Newton interior-point algorithm presented by Mansouri et al. [A full-Newton step [Formula: see text] infeasible interior-point algorithm for linear complementarity problems, Nonlinear Anal. Real World Appl. 12 (2011) 545–561] for monotone linear complementarity problems (MLCPs). In each iteration of Mansouri’s algorithm two types of full-Newton steps are used, one feasibility step and some ordinary (centering) steps. In this paper, we use a new search direction, and reduce the number of the centering steps, so that only one centering step is needed. We prove that the complexity of the algorithm is as good as the best-known complexity for infeasible interior-point methods for MLCPs.

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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