Deep Learning the Efficient Frontier of Convex Vector Optimization Problems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914815963824128 |
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| author | Feinstein, Zachary Rudloff, Birgit |
| author_facet | Feinstein, Zachary Rudloff, Birgit |
| contents | In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07077 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deep Learning the Efficient Frontier of Convex Vector Optimization Problems Feinstein, Zachary Rudloff, Birgit Optimization and Control Mathematical Finance Risk Management In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality. |
| title | Deep Learning the Efficient Frontier of Convex Vector Optimization Problems |
| topic | Optimization and Control Mathematical Finance Risk Management |
| url | https://arxiv.org/abs/2205.07077 |