MSRI Summer Graduate Workshops:

Continuous Optimization and Applications Workshop

July 9, 2007 to July 20, 2007

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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 using the NEOS Server for Optimization and the large group of NEOS Solvers. Solution interpretation and sensitivity analysis will be emphasized.

The workshop is divided into three series of lectures and hands-on labs.

  1. 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 ( Rockafellar, 1993)

  2. 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.
  3. 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 Engineering Problems. We will study and use several current solvers that are in the public domain.

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