1. General
introduction to nonlinear programming methods including the following algorithms for unconstrained
optimization:
- steepest descent,
- conjugate gradient,
- Newton, and pseudo Newton algorithms and
solution of
nonlinear vector equations.
2. Introduction to the linear least squared
error problem;
projections and null spaces.
3. Introduction
to constrained optimality :
- development of the necessary condition for
the convex case ,
- convex duality; the perturbation function
and dual function for
equality constraints ,
- extension to the case of mixed equality and inequality constraints
,
- feasible direction algorithm .
4. Topics
chosen and presented by the students.
5. Introduction
to nonlinear dynamic optimization :
- existence theory of optimal control
solutions ,
- the relaxed control problem,
- special properties of linear control
problems,
- the Pontryagin Maximum Principle,
- problems in the calculus of variations,
-
sufficiency of the Maximum principle.
Lecturer's
notes are a basis for the course and will be
distributed
in the class.
1. D.
P. Bertsekas, "Nonlinear Programming", Athena Scientific
Publisher,1995. [T57.8 B47 1995]
2. D.
P. Bertsekas, "Dynamic Programming and Optimal Control", Athena
Scientific Publisher, 1995. [T57.83 B476 1995]
3. E.
Polak, "Computational Methods in Optimization", lecture notes handed
out at University of California at Berkeley.
[QA402.5
P58]