scholarly journals The Mehrotra Predictor-Corrector Interior-Point Method As a Perturbed Composite Newton Method

1996 ◽  
Vol 6 (1) ◽  
pp. 47-56 ◽  
Author(s):  
R. Tapia ◽  
Y. Zhang ◽  
M. Saltzman ◽  
A. Weiser
Keyword(s):  
Newton Method ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Predictor Corrector

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 Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Antonio Roberto Balbo ◽  
Márcio Augusto da Silva Souza ◽  
Edméa Cássia Baptista ◽  
Leonardo Nepomuceno
Keyword(s):  
Power Systems ◽  
Interior Point ◽  
Interior Point Method ◽  
Line Search ◽  
Economic Dispatch ◽  
Point Method ◽  
Computational Implementation ◽  
Quadratic Programming Problems ◽  
Primal Dual ◽  
Predictor Corrector

This paper proposes a predictor-corrector primal-dual interior point method which introduces line search procedures (IPLS) in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch (ED) problem studied in the field of power systems analysis. The theory of the method is examined for quadratic programming problems and involves the analysis of iterative schemes, computational implementation, and issues concerning the adaptation of the proposed algorithm to solve ED problems. Numerical results are presented, which demonstrate improvements and the efficiency of the IPLS method when compared to several other methods described in the literature. Finally, postoptimization analyses are performed for the solution of ED problems.

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