interior point method
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2022 ◽  
Vol 10 (1) ◽  
Author(s):  
Yogi Jentrapolta Siregar ◽  
Lukmanul Hakim ◽  
Osea Zebua ◽  
Khairudin Hasan

Beberapa tahun terakhir, pada sistem tenaga listrik beban yang ada semakin besar seiring peningkatan beban listrik. Permasalahan utama kondisi pembebanan akan menyebabkan ketidakstabilan tegangan di sistem tenaga listrik. Untuk mencegah ketidakstabilan sistem, penting bagi operator sistem tenaga untuk mengidentifikasi seberapa jauh sistem memuat dari kondisi kritisnya. Penelitian ini membahas masalah maksimum pembebanan dengan menggunakan metode non-linear primal-dual interior point method. Caranya dengan memaksimalkan beban sistem yang diwakili oleh pengganda skalar ke beban sistem. Kontribusi utama dari pekerjaan ini adalah dalam pengembangan model vectorized dari masalah dan pengembangan program aplikasi dalam bahasa pemrograman Pyhton. Model yang dikembangkan kemudian diuji untuk memecahkan masalah loadability maksimum untuk sistem pengujian IEEE 14-bus dan 30-bus. Simulasi dari model ini dan program komputer yang dikembangkan memberikan hasil yang memuaskan.Kata Kunci : Python, Interior Point Method. Loadability Maksimum, dan Model Vectorized


2021 ◽  
Author(s):  
Jacek Gondzio ◽  
Matti Lassas ◽  
Salla-Maaria Latva-Äijö ◽  
Samuli Siltanen ◽  
Filippo Zanetti

Abstract Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined in space, but at any given location there is only one material present. Further, two X-ray energies are chosen so that there is a clear difference in the spectral dependence of the attenuation coefficients of the two materials. A novel regularizer is presented for the inverse problem of reconstructing separate tomographic images for the two materials. A combination of two things, (a) non-negativity constraint, and (b) penalty term containing the inner product between the two material images, promotes the presence of at most one material in a given pixel. A preconditioned interior point method is derived for the minimization of the regularization functional. Numerical tests with digital phantoms suggest that the new algorithm outperforms the baseline method, Joint Total Variation regularization, in terms of correctly material-characterized pixels. While the method is tested only in a two-dimensional setting with two materials and two energies, the approach readily generalizes to three dimensions and more materials. The number of materials just needs to match the number of energies used in imaging.


2021 ◽  
Vol 66 (4) ◽  
pp. 783-792
Author(s):  
Selma Lamri ◽  
◽  
Bachir Merikhi ◽  
Mohamed Achache ◽  
◽  
...  

In this paper, a weighted logarithmic barrier interior-point method for solving the linearly convex constrained optimization problems is presented. Unlike the classical central-path, the barrier parameter associated with the per- turbed barrier problems, is not a scalar but is a weighted positive vector. This modi cation gives a theoretical exibility on its convergence and its numerical performance. In addition, this method is of a Newton descent direction and the computation of the step-size along this direction is based on a new e cient tech- nique called the tangent method. The practical e ciency of our approach is shown by giving some numerical results.


Author(s):  
Riley Badenbroek ◽  
Etienne de Klerk

We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based a sketch of a universal interior point method using the so-called entropic barrier. It is well known that the gradient and Hessian of the entropic barrier can be approximated by sampling from Boltzmann-Gibbs distributions and the entropic barrier was shown to be self-concordant. The analysis of our algorithm uses properties of the entropic barrier, mixing times for hit-and-run random walks, approximation quality guarantees for the mean and covariance of a log-concave distribution, and results on inexact Newton-type methods.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2906
Author(s):  
Jaroslav Haslinger ◽  
Radek Kučera ◽  
Kristina Motyčková ◽  
Václav Šátek

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.


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