Mini-Course on PDE-Constrained Optimization, May 23-27, 2011

Course Description

The course is designed to present practical solutions for optimization problems with partial differential equations as constraints. The course is made of lectures and exercises that use realistic problems and, for some cases, real data. Code will be written in matlab. The course is divided to 16 lectures.

Course Notes:

Daily Schedule

Monday
10:00AM - 12:00PM

Lecture 1-2:

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Introduction - what type of problems are considered, where do they come from, what are computational issues.

Model Problems - We will consider 3 model problems

  • An elliptic model problem of finding the conductivity and source in a Poisson like equation
  • A parabolic problem of finding a boundary conditions on one side given measure- ments of the solution in another part
  • As inverse wave equation in frequency (we may have time to exploit this in time)
12:00PM - 2:00PM Lunch Break
2:00PM - 4:00PM

Lecture 3-4

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Discretization of the forward problem using finite volume and some discussion on finite element

Tuesday
10:00AM - 12:00PM

Lecture 5-7

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Sensitivity computation, Unconstrained optimization techniques

12:00PM - 2:00PM Lunch Break
2:00PM - 4:00PM

Lecture 8

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Bound constraints and examples

Wednesday
10:00AM - 12:00PM

Lecture 9-10

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Constrained optimization formulation
12:00PM - 2:00PM Lunch Break
2:00PM - 4:00PM

Lecture 11-12

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Regularization techniques, Regularization parameter selection
Thursday
No Class
Friday
10:00AM - 12:00PM

Lecture 13-14

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Statistical inference in parameter estimation, Experimental design
12:00PM - 2:00PM Lunch Break
2:00PM - 4:00PM

Lecture 15-16

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Problems with multiple right hand sides, Open questions and Summary