A Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for linear programming over symmetric cones

2015 ◽  
Vol 72 (4) ◽  
pp. 915-936 ◽  
Author(s):  
Ximei Yang ◽  
Yinkui Zhang ◽  
Hongwei Liu ◽  
Yonggang Pei
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Symmetric Cones ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

A wide neighborhood predictor–corrector infeasible-interior-point method for Cartesian P∗(κ)-LCP over symmetric cones

2016 ◽  
Vol 09 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Marzieh Sayadi Shahraki ◽  
Maryam Zangiabadi ◽  
Hossein Mansouri
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Jordan Algebras ◽  
Point Method ◽  
Symmetric Cones ◽  
Wide Neighborhood ◽  
Euclidean Jordan Algebras ◽  
Iteration Bound ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we present a predictor–corrector infeasible-interior-point method based on a new wide neighborhood of the central path for linear complementarity problem over symmetric cones (SCLCP) with the Cartesian [Formula: see text]-property. The convergence of the algorithm is proved for commutative class of search directions. Moreover, using the theory of Euclidean Jordan algebras and some elegant tools, the iteration bound improves the earlier complexity of these kind of algorithms for the Cartesian [Formula: see text]-SCLCPs.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

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