scholarly journals Implementation of the Full-Newton Step Algorithm for Weighted Linear Complementarity Problems

2021 ◽  
Vol 15 (1) ◽  
pp. 15-18
Author(s):  
Zsolt Darvay ◽  
Attila-Szabolcs Orbán
Keyword(s):  
Linear Complementarity Problems ◽  
Path Following ◽  
Linear Complementarity ◽  
Point Of View ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
C Programming Language ◽  
C Programming ◽  
Step Algorithm ◽  
Full Newton Step

Abstract We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from the implementation point of view. We studied two variants, which differ only in the method of updating the parameter which characterizes the central path. The implementation was done in the C++ programming language and the obtained numerical results prove the efficiency of the proposed method.

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.

scholarly journals Implementation of an Interior-point Algorithm for Linear Complementarity Problem Working in a Wide Neighborhood

2019 ◽  
Vol 11 (1) ◽  
pp. 47-50
Author(s):  
Zsolt Darvay ◽  
Attila-Szabolcs Orbán
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Point Of View ◽  
Interior Point Algorithm ◽  
C Programming Language ◽  
C Programming ◽  
Theoretical Results

Abstract In this article, we study the interior-point algorithm for solving linear complementarity problems, published by Xiaouje Ma, Hongwei Liu, Jianke Zhang and Weijie Cong from the implementation point of view. The algorithm was implemented in C++ programming language, thus supporting the effectiveness of the method. Despite the fact that the theoretical results refer only to the monotone linear complementarity problem, practical testing showed that the algorithm also works well in more general cases.

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.

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 Numerical Results for the General Linear Complementarity Problem

2019 ◽  
Vol 11 (1) ◽  
pp. 43-46
Author(s):  
Zsolt Darvay ◽  
Ágnes Füstös
Keyword(s):  
Programming Language ◽  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Results ◽  
Interior Point Algorithm ◽  
C Programming Language ◽  
C Programming

Abstract In this article we discuss the interior-point algorithm for the general complementarity problems (LCP) introduced by Tibor Illés, Marianna Nagy and Tamás Terlaky. Moreover, we present a various set of numerical results with the help of a code implemented in the C++ programming language. These results support the efficiency of the algorithm for both monotone and sufficient LCPs.

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