Lecture Notes: Convex Optimization
arXiv:2607.11664
summary
These lecture notes introduce the theory and algorithms of convex optimization, covering existence results, projected subgradient descent, proximal‑gradient and accelerated gradient methods, primal‑dual schemes, and a brief overview of optimal transport.
Abstract
Lecture notes for a course on convex optimization taught by Andreas Habring at Graz University of Technology in 2026. The notes cover mathematical preliminaries, fundamental results about existence and of solutions for minimization problems, projected subgradient descent, proximal-gradient methods, heavy ball gradient descent, Nesterov accelerated gradient descent and FISTA, primal-dual methods, and a short intro to optimal transport.
Topics & keywords
#convex optimization#gradient methods#proximal algorithms#primal-dual methods#optimal transportprojected subgradient descentproximal gradientheavy ball methodNesterov accelerated gradientFISTA