Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910344421572608 |
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| author | Milz, Johannes Ulbrich, Michael |
| author_facet | Milz, Johannes Ulbrich, Michael |
| contents | The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA critical points, we derive nonasymptotic sample size estimates for SAA critical points using the covering number approach. Thereby, we derive upper bounds on the number of samples needed to obtain accurate critical points of the risk-neutral PDE-constrained optimization problem through SAA critical points. We quantify accuracy using expectation and exponential tail bounds. Numerical illustrations are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14755 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization Milz, Johannes Ulbrich, Michael Optimization and Control 90C15, 90C30, 90C60, 49J20, 49J55, 49K45, 49K20, 35J61 The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA critical points, we derive nonasymptotic sample size estimates for SAA critical points using the covering number approach. Thereby, we derive upper bounds on the number of samples needed to obtain accurate critical points of the risk-neutral PDE-constrained optimization problem through SAA critical points. We quantify accuracy using expectation and exponential tail bounds. Numerical illustrations are presented. |
| title | Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization |
| topic | Optimization and Control 90C15, 90C30, 90C60, 49J20, 49J55, 49K45, 49K20, 35J61 |
| url | https://arxiv.org/abs/2207.14755 |