scholarly journals Solving non-linear portfolio optimization problems with the primal-dual interior point method

2007 ◽  
Vol 181 (3) ◽  
pp. 1019-1029 ◽  
Author(s):  
Jacek Gondzio ◽  
Andreas Grothey
Keyword(s):  
Portfolio Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Point Method ◽  
Non Linear ◽  
Primal Dual

A Noise Based Distributed Optimization Method for Multirobot Task Allocation With Multimodal Utility

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Baisravan HomChaudhuri ◽  
Manish Kumar
Keyword(s):  
Interior Point ◽  
Task Allocation ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Distributed Optimization ◽  
Computation Time ◽  
Point Method ◽  
Search Direction ◽  
Local Optima ◽  
Primal Dual

Distributed optimization methods have been used extensively in multirobot task allocation (MRTA) problems. In distributed optimization domain, most of the algorithms are developed for solving convex optimization problems. However, for complex MRTA problems, the cost function can be nonconvex and multimodal in nature with more than one minimum or maximum points. In this paper, an effort has been made to address these complex MRTA problems with multimodal cost functions in a distributed manner. The approach used in this paper is a distributed primal–dual interior point method where noise is added in the search direction as a mechanism to allow the algorithm to escape from suboptimal solutions. The search direction from the distributed primal–dual interior point method and the weighted variable updates help in the generation of feasible primal and dual solutions and in faster convergence while the noise added in the search direction helps in avoiding local optima. The optimality and the computation time of this proposed method are compared with that of the genetic algorithm (GA) and the numerical results are provided in this paper.

scholarly journals Pemodelan Vektor Metode Interior Point Untuk Studi Pembebanan Maksimum Sistem Tenaga Listrik

2022 ◽  
Vol 10 (1) ◽  
Author(s):  
Yogi Jentrapolta Siregar ◽  
Lukmanul Hakim ◽  
Osea Zebua ◽  
Khairudin Hasan
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Non Linear ◽  
Primal Dual

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

Advanced Primal-Dual Interior-Point Method for the Method of Moving Asymptotes

2018 ◽  
Author(s):  
Daozhong Li ◽  
Stephen Roper ◽  
Il Yong Kim
Keyword(s):  
Topology Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Point Method ◽  
Topology Optimization Problem ◽  
Method Of Moving Asymptotes ◽  
Primal Dual ◽  
Numerical Performance ◽  
Moving Asymptotes

The Method of Moving Asymptotes (MMA) is one of the well-known optimization algorithms for topology optimization due to its stable numerical performance. Here, this paper simplifies the MMA algorithm by considering the features of topology optimization problem statements and presents a strategy to solve the necessary subproblems based on the primal-dual-interior-point method to further enhance numerical performance. A new scaling mechanism is also introduced to improve searching quality by utilizing the sensitivities of the original problems at the beginning of each MMA iteration. Numerical examples of solving both mathematical problems and topology optimization problems demonstrate the success of this method.

New complexity analysis of a full Nesterov–Todd step interior-point method for semidefinite optimization

2017 ◽  
Vol 10 (04) ◽  
pp. 1750070 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Path Following ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Line Searches ◽  
Complexity Result ◽  
Primal Dual

In this paper, we propose a new primal-dual path-following interior-point method for semidefinite optimization based on a new reformulation of the nonlinear equation of the system which defines the central path. The proposed algorithm takes only full Nesterov and Todd steps and therefore no line-searches are needed for generating the new iterations. The convergence of the algorithm is established and the complexity result coincides with the best-known iteration bound for semidefinite optimization problems.

scholarly journals Evaluation of Transfer Capability based on Load Supplying Capability Calculation Using Primal-Dual Interior Point Method

2000 ◽  
Vol 120 (8-9) ◽  
pp. 1175-1181
Author(s):  
Min-Hwa Jeong ◽  
Junji Kubokawa ◽  
Naoto Yorino ◽  
Hiroshi Sasaki ◽  
Byongjun Lee ◽  
...  
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Transfer Capability ◽  
Primal Dual
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