Description
The main algorithms and software for constrained
optimization, emphasizing the sparse-matrix methods needed
for their implementation. Iterative methods for linear
equations and least squares. Interior methods. The simplex
method. Basis factorization and updates. The
reduced-gradient method, augmented Lagrangian methods, and
SQP methods.
3 units, Spring (Michael Saunders), Grading basis ABCD/NP
Prerequisites: Basic numerical linear algebra, including LU, QR,
and SVD factorizations, and an interest in MATLAB, sparse-matrix methods,
and algorithms for constrained optimization
Homework, etc
There will be 4 or 5 homework assignments and one somewhat more
challenging project. MATLAB is used for computational exercises.
Last year's project involved experiments with LSQR on
least-squares problems, using sparse LU factors to
construct a preconditioner. We will have a different
project this year -- again something to do with sparse matrices
and optimization.
Grades will be assessed from the homework and project.
There will be no final exam.
There is no text book for the class. The "References" link
is background reading and a reminder of some of the sources out there.
Location
Auditors are welcome