Nonlinear Convex Optimization with Applications in Imaging and Vision

Undergraduate and Graduate course, University of Siegen, 2025

Summer term 2025 (~ 4 students per semester).

  • Convex sets and functions

  • Gradient descent and its convergence

  • Variants: projected, proximal, and forward-backward splitting

  • Newton and quasi-Newton methods

  • Subdifferentials and KKT conditions

  • Quadratic programming and interior point methods

  • Duality and sequential quadratic programming

  • Nonsmooth Newton methods: NCP, patchwise, semismooth

  • Primal-dual hybrid gradient methods

  • Proximal Newton methods for unconstrained problems