Dual Spectral Projected Gradient Method for Generalized Log-det Semidefinite Programming
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913522699468800 |
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| author | Namchaisiri, Charles Yamashita, Makoto |
| author_facet | Namchaisiri, Charles Yamashita, Makoto |
| contents | Log-det semidefinite programming (SDP) problems are optimization problems that often arise from Gaussian graphic models. A log-det SDP problem with an l1-norm term has been examined in many methods, and the dual spectral projected gradient (DSPG) method by Nakagaki et al.~in 2020 is designed to efficiently solve the dual problem of the log-det SDP by combining a non-monotone line-search projected gradient method with the step adjustment for positive definiteness. This paper extends the DSPG method for solving a generalized log-det SDP problem involving additional terms to cover more structures in Gaussian graphical models in a unified style. We establish the convergence of the proposed method to the optimal value. We conduct numerical experiments to illustrate the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dual Spectral Projected Gradient Method for Generalized Log-det Semidefinite Programming Namchaisiri, Charles Yamashita, Makoto Optimization and Control 90C22, 90C25, 90C26 Log-det semidefinite programming (SDP) problems are optimization problems that often arise from Gaussian graphic models. A log-det SDP problem with an l1-norm term has been examined in many methods, and the dual spectral projected gradient (DSPG) method by Nakagaki et al.~in 2020 is designed to efficiently solve the dual problem of the log-det SDP by combining a non-monotone line-search projected gradient method with the step adjustment for positive definiteness. This paper extends the DSPG method for solving a generalized log-det SDP problem involving additional terms to cover more structures in Gaussian graphical models in a unified style. We establish the convergence of the proposed method to the optimal value. We conduct numerical experiments to illustrate the efficiency of the proposed method. |
| title | Dual Spectral Projected Gradient Method for Generalized Log-det Semidefinite Programming |
| topic | Optimization and Control 90C22, 90C25, 90C26 |
| url | https://arxiv.org/abs/2409.19743 |