MATH E-216 Convexity and Optimization with Applications

This course 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 are expected to understand and invent proofs of theorems in real and functional analysis. Prerequisites: MATH E-21a and MATH E-21b, or the equivalent, plus at least one other more advanced course in mathematics. (4 credits)