상세정보
Export to Refworks부가기능
Analyzing Sampling in Stochastic Optimization: Importance Sampling and Statistical Inference
상세 프로파일
| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Analyzing Sampling in Stochastic Optimization: Importance Sampling and Statistical Inference. |
| 개인저자 | Yu, Yang. |
| 단체저자명 | The University of North Carolina at Chapel Hill. Statistics and Operations Research. |
| 발행사항 | [S.l.]: The University of North Carolina at Chapel Hill., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 113 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088306994 |
| 학위논문주기 | Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Lu, Shu |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | The objective function of a stochastic optimization problem usually involves an expectation of random variables which cannot be calculated directly. When this is the case, a common approach is to replace the expectation with a sample average approximation. However, sometimes there are difficulties in using such a sample average approximation to achieve certain goals. This dissertation studies two specific problems. In the first problem, we aim to solve a minimization problem whose objective function is the probability of an undesired rare event. To accurately estimate this rare event probability by Monte Carlo simulation, an extremely large sample is required, which is expensive to implement. An importance sampling scheme based on the theory of large deviations is developed to efficiently reduce the sample size and thus reduce the computational cost. The convergence of a sequence of approximation problems is also studied, through which a good initial point to the minimization problem can be found. We also study the buffered probability of exceedance as an alternative risk measure instead of the ordinary probability. Under conditions, the analogous minimization problem can be formulated into a convex problem.In the second problem, we focus on a two-stage stochastic linear programming problem, where the objective function has to be approximated by a sample average function with a random sample of the corresponding random variables. However, such a sample average function is not smooth enough to estimate the Hessian of the objective function which is needed to calculate the confidence intervals for the true solution. To overcome this difficulty, the sample average function is smoothed by its convolution with a kernel function. Methods to compute confidence intervals for the true solution are then developed based on inference methods for stochastic variational inequalities. |
| 일반주제명 | Operations research. Monte Carlo simulation. Linear programming. Statistical inference. Stochastic models. Optimization. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
