Probable Event Constrained Optimization and A Data-embedded Solution Paradigm
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913720532205568 |
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| author | Li, Qifeng |
| author_facet | Li, Qifeng |
| contents | This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints (PEC). This new type of constraint guarantees that optimal solutions are feasible for all uncertain events whose joint probabilities are greater than a user-defined threshold. The PEC can be used as an alternative to the conventional chance constraint, while the latter cannot guarantee the solution's feasibility to high-probability uncertain events. Given that the existing solution methods of optimization problems under uncertainty are not suitable for solving PECO problems, we develop a novel data-embedded solution paradigm that uses historical measurements/data of the uncertain parameters as input samples. This solution paradigm is conceptually simple and allows us to develop effective data-reduction schemes which reduce computational burden while preserving high accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_01119 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Probable Event Constrained Optimization and A Data-embedded Solution Paradigm Li, Qifeng Optimization and Control This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints (PEC). This new type of constraint guarantees that optimal solutions are feasible for all uncertain events whose joint probabilities are greater than a user-defined threshold. The PEC can be used as an alternative to the conventional chance constraint, while the latter cannot guarantee the solution's feasibility to high-probability uncertain events. Given that the existing solution methods of optimization problems under uncertainty are not suitable for solving PECO problems, we develop a novel data-embedded solution paradigm that uses historical measurements/data of the uncertain parameters as input samples. This solution paradigm is conceptually simple and allows us to develop effective data-reduction schemes which reduce computational burden while preserving high accuracy. |
| title | Probable Event Constrained Optimization and A Data-embedded Solution Paradigm |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2209.01119 |