March 30, 2017
from 12:00 PM - 02:00 PM
University of Toronto Institute for Aerospace Studies (UTIAS Lecture Hall)
4925 Dufferin St
North York, ON M3H5T6
Adjoint methods will be presented for partial differential equation constrained optimization problems. Such methods are efficient for problems with more design variables than constraints, which is typical of aerodynamic shape optimization problems based on computational fluid dynamics, for example. Several different perspectives on adjoint methods will be discussed. Emphasis will be on the discrete adjoint approach as opposed to the continuous approach.
This talk will focus on numerical algorithms for solving computationally expensive optimization problems under parameter uncertainty. An overview of probabilistic and non-probabilistic approaches for formulating optimization problems under uncertainty will be presented and the computational challenges that arise will be highlighted. We will briefly describe two promising approaches for solving a class of problems: (1) numerical schemes based on efficient stochastic partial differential equation solvers and (2) Bayesian robust optimization algorithms.
In this talk, we provide a brief overview of two optimization methods that deal with noisy data. In robust optimization, the problem parameters may be contaminated with uncertainty and the goal is to derive optimal solutions that are de-sensitized to the uncertainty. In inverse optimization, noisy observations corresponding to the output of an optimization problem are observed and the goal is to reverse engineer the problem parameters that generated the observations. In addition to presenting the basic theory, we will briefly illustrate the application of these methods to two problems in radiation-based cancer therapy.