An interior-point method for generalized linear-fractional programming

1995 ◽  
Vol 69 (1-3) ◽  
pp. 177-204 ◽  
Author(s):  
Yu. E. Nesterov ◽  
A. S. Nemirovskii
Keyword(s):  
Interior Point ◽  
Fractional Programming ◽  
Interior Point Method ◽  
Point Method ◽  
Linear Fractional Programming

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.

scholarly journals An interior point method for isogeometric contact

2014 ◽  
Vol 276 ◽  
pp. 589-611 ◽  
Author(s):  
İ. Temizer ◽  
M.M. Abdalla ◽  
Z. Gürdal
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method

Towards a fast and robust interior point method for power system applications

2004 ◽  
Vol 151 (5) ◽  
pp. 575 ◽  
Author(s):  
M.J. Rider ◽  
C.A. Castro ◽  
M.F. Bedrinana ◽  
A.V. Garcia
Keyword(s):  
Power System ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method
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