Summer Graduate School
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- 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.)
- 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 Engineering Problems. We will study and use several current solvers that are in the public domain.
- Main Course Page for the Summer Graduate Workshop
- Lecture Notes (PDF file)
- What is Optimization? (Optimization Tree at NEOS)
- Importance/Applications of Optimization
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
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