The bifurcation of constrained optimization optimal solutions and its applications
The appearance and disappearance of the optimal solution for the change of system parameters in optimization theory is a fundamental problem. This paper aims to address this issue by transforming the solutions of a constrained optimization problem into equilibrium points (EPs) of a dynamical system....
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023622?viewType=HTML |
| _version_ | 1797850980079894528 |
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| author | Tengmu Li Zhiyuan Wang |
| author_facet | Tengmu Li Zhiyuan Wang |
| author_sort | Tengmu Li |
| collection | DOAJ |
| description | The appearance and disappearance of the optimal solution for the change of system parameters in optimization theory is a fundamental problem. This paper aims to address this issue by transforming the solutions of a constrained optimization problem into equilibrium points (EPs) of a dynamical system. The bifurcation of EPs is then used to describe the appearance and disappearance of the optimal solution and saddle point through two classes of bifurcation, namely the pseudo bifurcation and saddle-node bifurcation. Moreover, a new class of pseudo-bifurcation phenomena is introduced to describe the transformation of regular and degenerate EPs, which sheds light on the relationship between the optimal solution and a class of infeasible points. This development also promotes the proposal of a tool for predicting optimal solutions based on this phenomenon. The study finds that the bifurcation of the optimal solution is closely related to the bifurcation of the feasible region, as demonstrated by the 5-bus and 9-bus optimal power flow problems. |
| first_indexed | 2024-04-09T19:10:20Z |
| format | Article |
| id | doaj.art-8f49c1f3c8c34468a7556a82fc924691 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T19:10:20Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-8f49c1f3c8c34468a7556a82fc9246912023-04-07T01:30:42ZengAIMS PressAIMS Mathematics2473-69882023-03-0185123731239710.3934/math.2023622The bifurcation of constrained optimization optimal solutions and its applicationsTengmu Li0Zhiyuan Wang1School of Electrical and Information Engineering, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, ChinaSchool of Electrical and Information Engineering, Tianjin University, No. 92 Weijin Road, Nankai District, Tianjin 300072, ChinaThe appearance and disappearance of the optimal solution for the change of system parameters in optimization theory is a fundamental problem. This paper aims to address this issue by transforming the solutions of a constrained optimization problem into equilibrium points (EPs) of a dynamical system. The bifurcation of EPs is then used to describe the appearance and disappearance of the optimal solution and saddle point through two classes of bifurcation, namely the pseudo bifurcation and saddle-node bifurcation. Moreover, a new class of pseudo-bifurcation phenomena is introduced to describe the transformation of regular and degenerate EPs, which sheds light on the relationship between the optimal solution and a class of infeasible points. This development also promotes the proposal of a tool for predicting optimal solutions based on this phenomenon. The study finds that the bifurcation of the optimal solution is closely related to the bifurcation of the feasible region, as demonstrated by the 5-bus and 9-bus optimal power flow problems.https://www.aimspress.com/article/doi/10.3934/math.2023622?viewType=HTMLbifurcationconstrained optimization problemparametric nonlinear programmingdynamic systems |
| spellingShingle | Tengmu Li Zhiyuan Wang The bifurcation of constrained optimization optimal solutions and its applications AIMS Mathematics bifurcation constrained optimization problem parametric nonlinear programming dynamic systems |
| title | The bifurcation of constrained optimization optimal solutions and its applications |
| title_full | The bifurcation of constrained optimization optimal solutions and its applications |
| title_fullStr | The bifurcation of constrained optimization optimal solutions and its applications |
| title_full_unstemmed | The bifurcation of constrained optimization optimal solutions and its applications |
| title_short | The bifurcation of constrained optimization optimal solutions and its applications |
| title_sort | bifurcation of constrained optimization optimal solutions and its applications |
| topic | bifurcation constrained optimization problem parametric nonlinear programming dynamic systems |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023622?viewType=HTML |
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