A Non-convex Optimization Approach of Searching Algebraic Degree Phase-type Representations for General Phase-type Distributions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909989165072384 |
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| author | Liu, Yujie Yao, Dacheng Zhang, Hanqin |
| author_facet | Liu, Yujie Yao, Dacheng Zhang, Hanqin |
| contents | For a continuous-time phase-type distribution, starting with its Laplace-Stieltjes transform, we obtain a necessary and sufficient condition for its minimal phase-type representation to have the same order as the algebraic degree of the Laplace-Stieltjes transform. To facilitate finding this minimal representation, we transform this condition equivalently into a quadratic nonconvex optimization problem, which can be effectively addressed using an alternating minimization algorithm. The algorithm convergence is also proved. Moreover, the method we develop for the continuous-time phase-type distributions can be directly used to the discrete-time phase-type distributions after establishing an equivalence between the minimal representation problems for continuous-time and discrete-times phase-type distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12673 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Non-convex Optimization Approach of Searching Algebraic Degree Phase-type Representations for General Phase-type Distributions Liu, Yujie Yao, Dacheng Zhang, Hanqin Optimization and Control Probability For a continuous-time phase-type distribution, starting with its Laplace-Stieltjes transform, we obtain a necessary and sufficient condition for its minimal phase-type representation to have the same order as the algebraic degree of the Laplace-Stieltjes transform. To facilitate finding this minimal representation, we transform this condition equivalently into a quadratic nonconvex optimization problem, which can be effectively addressed using an alternating minimization algorithm. The algorithm convergence is also proved. Moreover, the method we develop for the continuous-time phase-type distributions can be directly used to the discrete-time phase-type distributions after establishing an equivalence between the minimal representation problems for continuous-time and discrete-times phase-type distributions. |
| title | A Non-convex Optimization Approach of Searching Algebraic Degree Phase-type Representations for General Phase-type Distributions |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2409.12673 |