Professor:
Francisco N. C. Sobral
Room:
Room 211 Building F67
E-mail:
Teaching times:
Tuesdays (implementation discussions), Wednesdays and Fridays: 9:40 - 11:20
Room 107 Building F67 (Room 202 on Tuesdays)
Room 107 Building F67 (Room 202 on Tuesdays)
Extras
Content
Week 1
- Introduction ENG
- Nonlinear equations ENG
Week 2
- Newton and quasi-Newton methods ENG
- Linear convergence ENG
- Implementation details
newton_nleq.jl
The Moré, Garbow and Hillstrom test problems
Week 3
- Implementation details
QR update - Linear and quadratic convergence of Newton ENG
- Convergence of quasi-Newton ENG
- COLUMN and ICUM quasi-Newton methods - see pg. 107 of Martínez, 2000 or pg. 14 here.
Week 4
- Introduction to optimization ENG
- Unconstrained optimization ENG
- Line-search methods ENG
Week 5
- Newton with line search ENG
- Quasi-Newton BFGS with line search ENG
Week 6
- Implementation of ICUM
- Performance profiles: Dolan, Moré (2002) and A note on performance profiles(2016)
- Comparing solvers for nonlinear systems
- Line searches ENG
- Practical stopping criteria ENG
- Introduction to trust region algorithms ENG
Week 7
- The trust region algorithm ENG
- Computing the step: Dogleg, Subspace and Steihag's algorithm ENG
- The Cauchy point ENG
Week 8
- Introduction to performance profiles
- Convergence of trust-region algorithms ENG
- Non-Euclidean norms for trust region ENG
Week 9
- Linear Conjugate Gradients ENG
- An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
- Introduction to Nonlinear Conjugate Gradients ENG
Week 10
- Convergence rate of CG and preconditioners
- Examples of constrained optimization problems ENG
Week 11
- First-order conditions in constrained optimization ENG
- Constraint qualifications ENG
- Class: First order conditions V3
Week 12
- KKT conditions ENG
- Projected gradient methods ENG
- Book: Opúsculo - J. M. Martínez
- Class: Projected gradient V4
Week 14
- Implementation
Week 15
- Spectral Projected Gradient ENG
- Hock-Schittkowski test set for constrained optimization
Week 16
- Implementation discussions
- Gencan ENG
- Introduction to Augmented Lagrangians ENG
- Class: Augmented Lagrangian V1
Week 17
- Convergence of trust region algorithms for box constrained problems
- Code
Last Update: November, 27 2019.