Introduction to normed, Banach and Hilbert spaces; applications of the projection theorem and the Hahn-Banach theorem to problems of minimum norm, mathematical programming, and optimal control; the Kuhn-Tucker theorem and Pontryagin's maximum principle; introduction to iterative methods.

• Normed vector spaces
• Iterative methods, fixed-point theorems
• Hilbert spaces - the projection theorem
• Hahn-Banach theorem: minimum norm problems
• Optimization problems in Hilbert and Banach spaces
• Local and global theory of constrained optimization: nonlinear programming and the Kuhn-Tucker theorem; optimal control and Pontryagin's minimum principle

D.G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, 1969.

MATH 315 or 383 and MATH 347, or consent of instructor. ECE 390 or MATH 384 desirable but not essential.

1 unit.

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