Impact of different central path neighborhoods on gross error identification in State Estimation with generalized correntropy interior point method

2019 ◽  
Author(s):  
Hamed Moayyed ◽  
Shabnam Pesteh ◽  
Vladimiro Miranda ◽  
Jorge Pereira
Keyword(s):  
State Estimation ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Central Path ◽  
Error Identification ◽  
Gross Error

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.

Simplified analysis of a full Nesterov–Todd step infeasible interior-point method for symmetric optimization

2015 ◽  
Vol 08 (04) ◽  
pp. 1550071 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Point Method ◽  
Central Path ◽  
Complexity Bound ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Infeasible Interior Point Method ◽  
Simplified Analysis

We give a simplified analysis and an improved iteration bound of a full Nesterov–Todd (NT) step infeasible interior-point method for solving symmetric optimization. This method shares the features as, it (i) requires strictly feasible iterates on the central path of a perturbed problem, (ii) uses the feasibility steps to find strictly feasible iterates for the next perturbed problem, (iii) uses the centering steps to obtain a strictly feasible iterate close enough to the central path of the new perturbed problem, and (iv) reduces the size of the residual vectors with the same speed as the duality gap. Furthermore, the complexity bound coincides with the currently best-known iteration bound for full NT step infeasible interior-point methods.

An interior point method for WLAV state estimation of power system with UPFCs

2010 ◽  
Vol 32 (6) ◽  
pp. 671-677 ◽  
Author(s):  
Chawasak Rakpenthai ◽  
Suttichai Premrudeepreechacharn ◽  
Sermsak Uatrongjit ◽  
Neville R. Watson
Keyword(s):  
Power System ◽  
State Estimation ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method

scholarly journals A Full Nesterov-Todd Step Infeasible Interior-point Method for Symmetric Optimization in the Wider Neighborhood of the Central Path

2021 ◽  
Vol 9 (2) ◽  
pp. 250-267
Author(s):  
Lesaja Goran ◽  
G.Q. Wang ◽  
A. Oganian
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Symmetric Optimization ◽  
Statistical Disclosure Limitation ◽  
Starting Point ◽  
Linear Optimization Problems

In this paper, an improved Interior-Point Method (IPM) for solving symmetric optimization problems is presented. Symmetric optimization (SO) problems are linear optimization problems over symmetric cones. In particular, the method can be efficiently applied to an important instance of SO, a Controlled Tabular Adjustment (CTA) problem which is a method used for Statistical Disclosure Limitation (SDL) of tabular data. The presented method is a full Nesterov-Todd step infeasible IPM for SO. The algorithm converges to ε-approximate solution from any starting point whether feasible or infeasible. Each iteration consists of the feasibility step and several centering steps, however, the iterates are obtained in the wider neighborhood of the central path in comparison to the similar algorithms of this type which is the main improvement of the method. However, the currently best known iteration bound known for infeasible short-step methods is still achieved.

Sign in / Sign up

Export Citation Format

Share Document