Tutorial on Algorithms and Software for PDE-constrained Optimization

Monday, June 6, 2016 - 3:15pm - 4:30pm
Lind 305
Denis Ridzal (Sandia National Laboratories)
1) Formulation and notation.
-- Reduced-space and full-space formulations.
-- Vector spaces, inner products and duality.
-- Derivative operators.

2) Algorithms for reduced-space formulations.
-- Methods using line search:
- Gradient descent, nonlinear conjugate gradients;
- Quasi-Newton, Newton and Newton-Krylov methods.
-- Methods using trust regions:
- Cauchy-point and dogleg methods;
- Truncated conjugate gradient methods.
-- Treatment of inexact computations through trust regions.

3) Algorithms for full-space formulations.
-- Sequential quadratic programming:
- with line search;
- with trust regions.
-- Matrix-free composite-step methods.
-- Preconditioning of optimality systems.

4) Treatment of inequality constraints.
-- Augmented-Lagrangian methods.
-- Moreau-Yosida regularization.
-- Primal-dual active set or semismooth Newton methods.
-- Interior-point methods.

5) Software, illustrated through the Rapid Optimization Library (ROL).
-- A functional interface for optimization with simulation constraints.
-- A linear algebra interface for optimization with simulation constraints.
-- Example problems:
- linear elliptic control (the mother problem);
- the obstacle problem (control of VIs); and
- risk-averse topology optimization.
MSC Code: