This workshop is intended to introduce to graduate students the
main ideas of Continuous Optimization and its Applications.
In particular, we emphasize the major developments in the last ten
years. This includes the use of interior point methods in the solution
of large scale linear and nonlinear programs.
The workshop includes a hands-on approach. Numerical tests will be done
NEOS Server for Optimization and the large group of
Solution interpretation and sensitivity analysis will be emphasized.
The workshop is divided into three series of lectures and hands-on labs.
The first series includes an introduction to the modern theory of convex
programming, its extensions and applications. This includes
separation and support theorems, and Lagrange multiplier results.
This series emphasizes that:
the great watershed in optimization is not between linearity and
nonlinearity, but convexity and nonconvexity
The main series of lectures involves numerical algorithms for
general nonlinear optimization. This includes both modern interior point
approaches as well as classical Lagrange multiplier
methods such as sequential quadratic programming, SQP.
We include applications to engineering and financial problems and
emphasize the large scale case.
The final series concentrates on specialized topics and applications.
In particular, this includes optimization over convex sets
described as the intersections
of the set of symmetric, positive semidefinite matrices with affine
spaces, i.e. Semidefinite Programming.
This area has attracted a lot of interest due to the number of important
applications, to e.g. Discrete Optimization and more general
We will study and use several current solvers that are
in the public domain.