A Class of Polynomial Interior Point Algorithms for the Cartesian P-Matrix Linear Complementarity Problem over Symmetric Cones

2011 ◽  
Vol 152 (3) ◽  
pp. 739-772 ◽  
Author(s):  
G. Q. Wang ◽  
Y. Q. Bai
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Symmetric Cones ◽  
Interior Point Algorithms ◽  
P Matrix

A NEW POLYNOMIAL INTERIOR-POINT ALGORITHM FOR THE MONOTONE LINEAR COMPLEMENTARITY PROBLEM OVER SYMMETRIC CONES WITH FULL NT-STEPS

2012 ◽  
Vol 29 (02) ◽  
pp. 1250015 ◽  
Author(s):  
G. Q. WANG
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Euclidean Jordan Algebra ◽  
Linear Complementarity ◽  
Jordan Algebras ◽  
Symmetric Cones ◽  
Interior Point Algorithm ◽  
Euclidean Jordan Algebras ◽  
Iteration Bound

In this paper, we present a new polynomial interior-point algorithm for the monotone linear complementarity problem over symmetric cones by employing the framework of Euclidean Jordan algebras. At each iteration, we use only full Nesterov and Todd steps. The currently best known iteration bound for small-update method, namely, [Formula: see text], is obtained, where r denotes the rank of the associated Euclidean Jordan algebra and ε the desired accuracy.

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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