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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.02797 |
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| _version_ | 1866912804857970688 |
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| author | Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan |
| author_facet | Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan |
| contents | We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions including cross-entropy and Kullback-Leibler divergence. We propose a hierarchy of moment relaxations based on the truncated $K$-moment problems to solve log-polynomial optimization. We provide sufficient conditions for the hierarchy to be tight and introduce a numerical method to extract the global optimizers when the tightness is achieved. In addition, we modify relaxations with optimality conditions to better fit log-polynomial optimization with convenient Lagrange multipliers expressions. Various applications and numerical experiments are presented to show the efficiency of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02797 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-Polynomial Optimization Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan Optimization and Control We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions including cross-entropy and Kullback-Leibler divergence. We propose a hierarchy of moment relaxations based on the truncated $K$-moment problems to solve log-polynomial optimization. We provide sufficient conditions for the hierarchy to be tight and introduce a numerical method to extract the global optimizers when the tightness is achieved. In addition, we modify relaxations with optimality conditions to better fit log-polynomial optimization with convenient Lagrange multipliers expressions. Various applications and numerical experiments are presented to show the efficiency of our method. |
| title | Log-Polynomial Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.02797 |