Splitting Algorithms for Distributionally Robust Optimization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914994415730688 |
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| author | Briceño-Arias, Luis López-Rivera, Sergio Vilches, Emilio |
| author_facet | Briceño-Arias, Luis López-Rivera, Sergio Vilches, Emilio |
| contents | In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity operator of the supremum function that appears in the optimization problem. The second method solves an equivalent monotone inclusion formulation derived from the first-order optimality conditions, where the resolvents of the monotone operators involved in the inclusion are computable. The proposed methods are applied to solve the Couette inverse problem with uncertainty and the denoising problem with uncertainty. We present numerical results to compare the efficiency of the algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21398 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splitting Algorithms for Distributionally Robust Optimization Briceño-Arias, Luis López-Rivera, Sergio Vilches, Emilio Optimization and Control 47H05, 65K05, 90C15, 90C17, 90C25, 90C47 In this paper, we provide different splitting methods for solving distributionally robust optimization problems in cases where the uncertainties are described by discrete distributions. The first method involves computing the proximity operator of the supremum function that appears in the optimization problem. The second method solves an equivalent monotone inclusion formulation derived from the first-order optimality conditions, where the resolvents of the monotone operators involved in the inclusion are computable. The proposed methods are applied to solve the Couette inverse problem with uncertainty and the denoising problem with uncertainty. We present numerical results to compare the efficiency of the algorithms. |
| title | Splitting Algorithms for Distributionally Robust Optimization |
| topic | Optimization and Control 47H05, 65K05, 90C15, 90C17, 90C25, 90C47 |
| url | https://arxiv.org/abs/2410.21398 |