Title page for ETD etd-03252003-213320


Type of Document Master's Thesis
Author Vugrin, Kay E.
Author's Email Address kvugrin@vt.edu
URN etd-03252003-213320
Title On the Effect of Numerical Noise in Simulation-Based Optimization
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Borggaard, Jeffrey T. Committee Chair
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Sun, Shu-Ming Committee Member
Keywords
  • trust region algorithm
  • sensitivity analysis
  • shape optimization
Date of Defense 2003-03-12
Availability unrestricted
Abstract
Numerical noise is a prevalent concern in many practical optimization problems. Convergence of gradient based optimization algorithms in the presence of numerical noise is not always assured. One way to improve optimization algorithm performance in the presence of numerical noise is to adjust the method of gradient computation. This study investigates the use of Continuous Sensitivity Equation (CSE) gradient approximations in the context of numerical noise and optimization. Three problems are considered: a problem with a system of ODE constraints, a single parameter flow problem constrained by the Navier-Stokes equations, and a multiple parameter flow problem constrained by the Navier-Stokes equations. All three problems use adaptive methods in the simulation of the constraint and are numerically noisy. Gradients for each problem are computed with both CSE and finite difference methods. The gradients are analyzed and compared. The two flow problems are optimized with a trust region optimization algorithm using both sets of gradient calculations. Optimization results are also compared, and the CSE gradient approximation yields impressive results for these examples.

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