Brief Introduction to PDE-constrained Optimization

Monday, June 6, 2016 - 9:00am - 10:15am
Lind 305
Harbir Antil (George Mason University)
1) Basics: Problem statement, examples of elliptic/parabolic optimal control problems (OCP)
-Steps to solve an OCP: existence/uniqueness of solution; first­order necessary and second order sufficient optimality conditions; Numerical approximation and analysis of the discretized problem; Implementation of the discretized problem

2) Uniqueness and regularity of weak solution to elliptic BVPs.

3) Linear elliptic control problems:
-Reduced functional
-Differentiation in Banach spaces: Gateaux, Frechet
-First order necessary optimality conditions
-Formal Lagrange Method

4) Semilinear elliptic control problems
-Existence of solution to state equation and the control problem
-Nemytskii operator
-Differentiability of control to state map
-First order necessary conditions

5) Finite element discretization and provide a finite element solver
MSC Code: