A polynomial path-following interior point algorithm for general linear complementarity problems

2008 ◽  
Vol 47 (3) ◽  
pp. 329-342 ◽  
Author(s):  
Tibor Illés ◽  
Marianna Nagy ◽  
Tamás Terlaky
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Path Following ◽  
Linear Complementarity ◽  
General Linear ◽  
Interior Point Algorithm

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 Predictor-Corrector Interior-Point Algorithm for the General Linear Complementarity Problem

2021 ◽  
Vol 15 (1) ◽  
pp. 11-14
Author(s):  
Zsolt Darvay ◽  
Ágnes Füstös
Keyword(s):  
Interior Point ◽  
Large Scale ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Point Of View ◽  
General Linear ◽  
Interior Point Algorithm ◽  
Step Size ◽  
Predictor Corrector

Abstract We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. We analyze the method proposed by Illés, Nagy and Terlaky [1] that extends the algorithm published by Potra and Liu [2] to general linear complementarity problems. A new method for determining the step size of the corrector direction is presented. Using the code implemented in the C++ programming language, we can solve large-scale problems based on sufficient matrices.

scholarly journals An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

2018 ◽  
Vol 23 (1) ◽  
pp. 1-16
Author(s):  
Mohammad Pirhaji ◽  
Maryam Zangiabadi ◽  
Hossein Mansouri ◽  
Saman H. Amin
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Symmetric Cone ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Complexity Bound ◽  
Wide Neighborhood ◽  
Mathematical Problems

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.

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