Confidence Intervals for Stochastic Variational Inequalities

Public Deposited
Analytics

Downloadable Content

Download PDF
Request Version for Screen Reader
Last Modified
  • March 19, 2019
Creator
  • Lamm, Michael
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
Abstract
  • This dissertation examines the effects of uncertain data on a general class of optimization and equilibrium problems. The common framework used for modeling these problems is a stochastic variational inequality. Variational inequalities can be used to model conditions that characterize an equilibrium state, or describe necessary conditions for solutions to constrained optimization problems. For example, Cournot-Nash equilibrium problems and the Karush-Kuhn-Tucker conditions for nonlinear programming problems both fit in the framework of a variational inequality. Uncertain model data can be incorporated into a variational inequality through the use of an expectation function. A variational inequality defined in this manner is referred to as a stochastic variational inequality (SVI). For many problems of interest the SVI cannot be solved directly. This can be due to limited distributional information or an expectation function that lacks a closed form expression and is difficult to evaluate. When this is the case, the SVI must be replaced with a suitable approximation. A common approach is to solve a sample average approximation (SAA). The SAA problem is a variational inequality with the expectation function replaced by a function that depends on a sample of the uncertain data. A natural question is then how the solution of the SAA problem compares to the true solution of the SVI. To address this question, this dissertation examines the construction of simultaneous and individual confidence intervals for the true solution of an SVI.
Date of publication
Keyword
Subject
DOI
Identifier
Resource type
Rights statement
  • In Copyright
Advisor
  • Budhiraja, Amarjit
  • Lu, Shu
  • Provan, Scott
  • Pataki, Gabor
  • Kulkarni, Vidyadhar
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2015
Language
Publisher
Place of publication
  • Chapel Hill, NC
Access right
  • There are no restrictions to this item.
Date uploaded
  • August 25, 2015

Relations

Parents:

This work has no parents.

Items

Thumbnail Title Date Uploaded Visibility Actions
file details Lamm_unc_0153D_15469.pdf 2019-04-12 Public Download