A Modified-Newton Step Primal-dual Interior Point Algorithm for Linear Complementarity Problems

2011 ◽  
Vol 6 (10) ◽  
Author(s):  
Lipu Zhang ◽  
Yinghong Xu
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Primal Dual

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.

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 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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