The Extension of Auxiliary Problem Principle for Solving Dynamic Economic Dispatch Problem in Power Systems
In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an...
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| Vydané v: | Journal of Mathematics Ročník 2022; číslo 1 |
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| Jazyk: | English |
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Cairo
Hindawi
2022
John Wiley & Sons, Inc Wiley |
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| ISSN: | 2314-4629, 2314-4785 |
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| Abstract | In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m ≥ 3 is to extend the method of APP, resulting in the APP-like algorithm. The convergence of the APP-like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP-like algorithm. Specifically, the APP algorithm is a special case of the APP-like algorithm when m = 2. However, simulation results show that the convergence efficiency of the APP-like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP-like algorithm in this paper. Simulation results show that the improved APP-like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP-like algorithm is better when compared with the APP-like algorithm. |
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| AbstractList | In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m≥3 is to extend the method of APP, resulting in the APP-like algorithm. The convergence of the APP-like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP-like algorithm. Specifically, the APP algorithm is a special case of the APP-like algorithm when m=2. However, simulation results show that the convergence efficiency of the APP-like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP-like algorithm in this paper. Simulation results show that the improved APP-like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP-like algorithm is better when compared with the APP-like algorithm. In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m ≥ 3 is to extend the method of APP, resulting in the APP-like algorithm. The convergence of the APP-like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP-like algorithm. Specifically, the APP algorithm is a special case of the APP-like algorithm when m = 2. However, simulation results show that the convergence efficiency of the APP-like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP-like algorithm in this paper. Simulation results show that the improved APP-like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP-like algorithm is better when compared with the APP-like algorithm. In this paper, we study the convex optimization problem with linear constraint, and the objective function is composed of m separable convex functions. Considering the special case where the objective function is composed of two separable convex functions, the auxiliary problem principle (APP) is an effective parallel distributed algorithm for solving the special case. Inspired by the principle of APP, a natural idea to solve separable convex optimization problem with m ≥ 3 is to extend the method of APP, resulting in the APP‐like algorithm. The convergence of the APP‐like algorithm is not clear yet. In this paper, we give a sufficient condition for the convergence of the APP‐like algorithm. Specifically, the APP algorithm is a special case of the APP‐like algorithm when m = 2. However, simulation results show that the convergence efficiency of the APP‐like algorithm is affected by the selection of penalty parameter. Therefore, we propose an improved APP‐like algorithm in this paper. Simulation results show that the improved APP‐like algorithm is robust to the selection of penalty parameter and that the convergence efficiency of the improved APP‐like algorithm is better when compared with the APP‐like algorithm. |
| Audience | Academic |
| Author | Ren, Yaming |
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| Cites_doi | 10.1109/tpwrs.2013.2283175 10.3906/elk-1411-111 10.1109/tsg.2018.2873650 10.1360/012011-1049 10.1109/mper.2002.4312139 10.3390/mca21030035 10.1080/02331934.2011.611885 10.1093/imanum/drt060 10.1007/s10107-014-0826-5 10.1007/bf00934554 10.1137/110822347 10.1109/tvt.2020.3028089 10.1023/a:1013601906224 10.1016/0898-1221(76)90003-1 10.1155/2021/2497209 |
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| Copyright | Copyright © 2022 Yaming Ren. COPYRIGHT 2022 John Wiley & Sons, Inc. Copyright © 2022 Yaming Ren. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Algorithms Computational geometry Convergence Convex analysis Convexity Economic aspects Electric power systems Lagrange multiplier Mathematics Optimization Parameters Power dispatch Principles |
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| Title | The Extension of Auxiliary Problem Principle for Solving Dynamic Economic Dispatch Problem in Power Systems |
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