Bregman proximal gradient method for linear optimization under entropic constraints
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908996222320640 |
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| author | Briceño-Arias, Luis M. Treust, Maël Le |
| author_facet | Briceño-Arias, Luis M. Treust, Maël Le |
| contents | In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints, a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of active and inactive constraints, addressing each using a Bregman proximal gradient method with entropic Legendre functions, for which we establish a convergence rate of $O(1/n)$ in objective values. For a specific cost structure, our framework provides a theoretical justification for the well-known Blahut-Arimoto algorithm and the uniqueness of the Lagrange multiplier associated with the entropic constraint. In the active constraint setting, we include a bisection procedure to approximate the strictly positive Lagrange multiplier. The efficiency of the proposed method is illustrated through comparisons with standard optimization solvers on a representative example from game theory, including extensions to higher-dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bregman proximal gradient method for linear optimization under entropic constraints Briceño-Arias, Luis M. Treust, Maël Le Optimization and Control 90C25 and 65K05 In this paper, we present an efficient algorithm for solving a linear optimization problem with entropic constraints, a class of problems that arises in game theory and information theory. Our analysis distinguishes between the cases of active and inactive constraints, addressing each using a Bregman proximal gradient method with entropic Legendre functions, for which we establish a convergence rate of $O(1/n)$ in objective values. For a specific cost structure, our framework provides a theoretical justification for the well-known Blahut-Arimoto algorithm and the uniqueness of the Lagrange multiplier associated with the entropic constraint. In the active constraint setting, we include a bisection procedure to approximate the strictly positive Lagrange multiplier. The efficiency of the proposed method is illustrated through comparisons with standard optimization solvers on a representative example from game theory, including extensions to higher-dimensional settings. |
| title | Bregman proximal gradient method for linear optimization under entropic constraints |
| topic | Optimization and Control 90C25 and 65K05 |
| url | https://arxiv.org/abs/2506.10849 |