Nonlinear Programming (81-404), Summer 2002
Lectures (Christoph Helmberg): 4, Tue 11:45-13:15, Room 48-208, Wed 11:45-13:15, Room 48-210,
Tutorial (Berhanu Guta): 2, Fri 10:00-11:30, Room 48-438
Overview
We discuss basic algorithmic approaches for solving smooth
nonlinear optimization problems. Aspects of interest are convergence
rate, computational efficiency and numerical behavior.
| Part I | Unconstrained Optimization: line search, trust regions,
conjugate gradients, Newton and quasi-Newton methods,
approximate and automatic differentation |
| Part II | Constrained Optimization: Lagrange multipliers,
optimality conditions, quadratic programming, penalty
barrier and augmented Lagrangian methods, sequential
quadratic programming |
Literature
Main source: J. Nocedal, S.J. Wright; Numerical Optimization, Springer 1999;
Further reading:
Bazaraa, Sherali, Shetty; Nonlinear Programming: Theory and Algorithms, Wiley, 1993;
Luenberger; Linear and Nonlinear Programming, Addison-Wesley, 1984.
Exercises
- Exercises 1 (ps-file), distributed on 16.4., due on 23.4.
MATLAB example files: exercise1_1.m, exercise1_2.m
- Exercises 2 (ps-file), distributed on 23.4., due on 30.4.
MATLAB example file: exercise2_4.m
- Exercises 3 (ps-file), distributed on 30.4., due on 7.5.
To implement this for general functions in MATLAB, try help on "function", "fminbnd", and "feval". For output, check the commands "disp" and "sprintf".
- Exercises 4 (ps-file), distributed on 7.5., due on 14.5.
- Exercises 5 (ps-file), distributed on 14.5., due on 21.5.
- Exercises 6 (ps-file), distributed on 28.5., due on 4.6.
Use your CG-algorithm on matrices A and b in this gzipped .mat-file.
- Exercises 7 (ps-file), distributed on 4.6., due on 11.6.
- Exercises 8 (ps-file), distributed on 11.6., due on 18.6.
- Exercises 9 (ps-file), distributed on 18.6., due on 25.6.
- Exercises 10 (ps-file), distributed on 25.6., due on 2.7.
- Exercises 11 (ps-file), distributed on 3.7., due on 9.7.
- Exercises 12 (ps-file), distributed on 9.7., due on 16.7.
- Exercises 13 (ps-file), distributed on 16.7.
Last modified: Tue Jul 16 10:31:07 CEST 2002