Convex Analysis and Optimization
MIT OpenCourseWare's graduate course on convexity, duality, and convex optimization algorithms, taught through the lens of a small set of unifying geometric principles rather than case-by-case techniques. The syllabus covers convex sets and functions, conjugate duality, saddle point and minimax theory, Lagrange multipliers, and algorithms including subgradient, polyhedral approximation, and proximal methods, connecting them to Fenchel duality and nonlinear programming. Materials include lecture notes, problem sets with solutions, and readings drawn from Dimitri Bertsekas's texts on convex optimization. No video lectures are included, but the written notes are detailed enough to follow independently. Free to audit under MIT's open license, with no certificate offered. Intended for students with a solid background in analysis and linear algebra who want the theoretical foundations behind modern optimization methods used in engineering and machine learning.