A projected–gradient interior–point algorithm for complementarity problems

2010 ◽  
Vol 57 (4) ◽  
pp. 457-485 ◽  
Author(s):  
Roberto Andreani ◽  
Joaquim J. Júdice ◽  
José Mario Martínez ◽  
Joao Patrício
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Interior Point Algorithm ◽  
Projected Gradient

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.

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.

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.

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