An arc-search infeasible interior-point algorithm for horizontal linear complementarity problem in the N∞− neighbourhood of the central path

2017 ◽  
Vol 94 (12) ◽  
pp. 2271-2282
Author(s):  
B. Kheirfam
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Horizontal Linear Complementarity Problem

A primal-dual interior-point method based on a new kernel function for linear complementarity problem

2019 ◽  
Vol 12 (07) ◽  
pp. 2050001
Author(s):  
El Amir Djeffal ◽  
Mounia Laouar
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Small Neighborhood ◽  
Linear Complementarity ◽  
Central Path ◽  
Search Direction ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Primal Dual

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

A modified infeasible interior-point algorithm for P*(κ)-HLCP over symmetric cones

2016 ◽  
Vol 09 (02) ◽  
pp. 1650039
Author(s):  
Mohammad Pirhaji ◽  
Hossein Mansouri ◽  
Maryam Zangiabadi
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Interior Point Methods ◽  
Complexity Analysis ◽  
Linear Complementarity ◽  
Symmetric Cones ◽  
Interior Point Algorithm ◽  
Horizontal Linear Complementarity Problem ◽  
Iteration Bound

An improved version of infeasible interior-point algorithm for [Formula: see text] horizontal linear complementarity problem over symmetric cones is presented. In the earlier version (optimization, doi: 10.1080/02331934.2015.1062011) each iteration of the algorithm consisted of one so-called feasibility step and some centering steps. The main advantage of the modified version is that it uses only one feasibility step in each iteration and the centering steps not to be required. Furthermore, giving a complexity analysis of the algorithm, we derive the currently best-known iteration bound for infeasible interior-point methods.

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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