ECE 580

Optimization by Vector Space Methods

** Office : ** 356 CSL (Phone: 3-3607)

** Email : ** ` basar1@illinois.edu `

** Text : ** D. G. Luenberger, Optimization
by Vector Space Methods,
Wiley, 1997.

** Meeting times :** Tuesdays and Thursdays,
9:30 a.m. - 10:50 a.m. (possibly starting at 9:00 a.m. some weeks) in 4070 ECEB

COURSE OUTLINE

- An introduction to functional analytic approach to optimization; Finite- versus infinite-dimensional spaces; Application examples (1 hr)
- Normed linear spaces (3 hrs)
- Optimization of functionals -- General results on existence and uniqueness of an optimum (1 hr)
- Fixed points of transformations on Banach Spaces -- Applications to solutions of differential (ordinary and partial) and integral equations; Minimax and Nash equilibrium theorems of game theory (5 hrs)
- Hilbert Spaces -- The Projection Theorem; Minimum distance to a convex set (2 hrs)
- Examples of complete orthonormal sequences; Wavelets (2 hrs)
- Hilbert Spaces of random variables and stochastic processes; Least-squares estimation (3 hrs)
- Dual Spaces. The Hahn-Banach Theorem, with applications to minimum norm problems (5 hrs)
- Linear operators and adjoints (4 hrs)
- Calculus in Banach Spaces; Gateaux and Frechet derivatives. Local theory of unconstrained optimization; Euler-Lagrange equations (3 hrs)
- Global theory of unconstrained optimization; Fenchel duality theory (2 hrs)
- Constrained optimization of functionals; Local and global theory. Nonlinear programming and the Kuhn-Tucker Theorem in infinite dimensions (4 hrs)
- Optimal control and Pontryagin's Minimum Principle (3 hrs)
- Differential Games (2 hrs)
- Numerical Methods (1 hr)
- Other related topics of interest, such as artificial neural networks, infinite dimensional linear systems, H-infinity control for distributed parameter systems (as time permits)

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## Useful Information | ## Reserve Books |

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