You can find the full syllabus on the canvas site. We will use Piazza for questions exclusively.
Instructor: Professor Laura Balzano,
Course time: Tuesday/Thursday 10:30am-12pm
Course location: EECS 3427
Office hours: TBD EECS 4223
Textbook: Optimization by Vector Space Methods by Luenberger.
Tentative syllabus: Tentatively, we will cover the following topics in roughly this order.
Vector spaces - definition - subspaces, linear combinations, span - linear independence and basis - subspaces, cones, convexity - functions and mappings - vector spaces of mappings Metric spaces - topology - sequences and convergence in metric spaces - fixed points and contraction mappings - continuous functions Normed Vector spaces - Banach spaces - lp and Lp spaces - projections - applications (signal processing, control, optimization) Inner Product spaces - Hilbert spaces - orthogonal complement, orthogonality principle - function approximation - projections - applications (signal processing, control, optimization) Linear functions - Linear functionals - Dual space - Riesz Representation theorem - Hahn-Banach theorem - Linear operators - adjoint operators - solving linear equations Optimization of functionals - conjugate functional - Minkowski functional - Fenchel duality With time: Spectral theory - The Spectral theorem - eigenvalues and eigenvectors of integral operators Optimization using lagrange multipliers - sufficient conditions for arbitrary functions - convex functions - necessary conditions for convex functions - Gateaux derivative - Kuhn-Tucker sufficiency - Frechet derivative More results in optimization - Farkas lemma - Karush-Kuhn-Tucker theorem