scholarly journals A wide neighborhood primal-dual interior-point algorithm with arc-search for linear complementarity problems

2018 ◽  
Vol 2018 ◽  
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Wide Neighborhood ◽  
Primal Dual

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.

scholarly journals A new second-order corrector interior-point algorithm for P*(k)-LCP

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6379-6391 ◽  
Author(s):  
B. Kheirfam ◽  
M. Chitsaz
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Second Order ◽  
Interior Point Algorithm ◽  
Iteration Complexity ◽  
Improve Performance ◽  
Complexity Bound ◽  
Wide Neighborhood

In this paper, we propose a second-order corrector interior-point algorithm for solving P*(k)- linear complementarity problems. The method generates a sequence of iterates in a wide neighborhood of the central path introduced by Ai and Zhang. In each iteration, the method computes a corrector direction in addition to the Ai-Zhang direction, in an attempt to improve performance. The algorithm does not depend on the handicap k of the problem, so that it can be used for any P*(k)-linear complementarity problems. It is shown that the iteration complexity bound of the algorithm is O ((1+k)3 ? nL). Some numerical results are provided to illustrate the performance of the algorithm.

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