Mathematics 116

Real Analysis, Convexity, and Optimization (118302)

Paul Bamberg (he)

2024 Fall (4 Credits)

Schedule: F 1200 PM - 0245 PM

Instructor Permissions: None

Enrollment Cap: n/a

Develops the theory of convex sets, normed infinite-dimensional vector spaces, and convex functionals and applies it as a unifying principle to a variety of optimization problems such as resource allocation, production planning, and optimal control. Topics include Hilbert space, dual spaces, the Hahn-Banach theorem, the Riesz representation theorem, calculus of variations, and Fenchel duality. Students will be expected to understand and come up with proofs of theorems in real and functional analysis.

Recommended Prep:

Mathematics 22a,b, 23a,b or 25a,b or 55a,b; or Mathematics 21a,b plus at least one other more advanced course in mathematics; or an equivalent background in mathematics.

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