风险中性半线性 PDE 受限优化的样本量估计

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Optimization Pub Date : 2024-02-23 DOI:10.1137/22m1512636

Johannes Milz, Michael Ulbrich

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引用次数: 0

摘要

SIAM 优化期刊》第 34 卷第 1 期第 844-869 页，2024 年 3 月。摘要。样本平均近似（SAA）方法适用于由随机输入的半线性椭圆偏微分方程控制的风险中性优化问题。在构建了包含 SAA 临界点的紧凑集之后，我们利用覆盖数方法推导出了 SAA 临界点的非渐近样本大小估计值。因此，我们推导出了通过 SAA 临界点获得风险中性 PDE 受限优化问题准确临界点所需的样本数量上限。我们使用期望值和指数尾边界来量化精确度。并给出了数值说明。

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Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

SIAM Journal on Optimization, Volume 34, Issue 1, Page 844-869, March 2024.
Abstract. 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.

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来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.