Short Courses

Technical University of Denmark, August 23–27, 2010

Algorithms for large-scale convex optimization

Lecture notes

• Lecture 1. Convex optimization theory: convex sets and functions, subgradients, conjugate function, duality

• Lecture 2. Unconstrained optimization methods: Newton and quasi-Newton methods, gradient method, conjugate gradient method, subgradient method

• Lecture 3. Proximal gradient method: proximal operator, proximal gradient method and applications, convergence analysis, accelerated proximal gradient method

• Lecture 4: Dual methods: dual decomposition, network optimization examples, dual proximal gradient method, augmented Lagrangian method

• Lecture 5: Primal-dual interior-point methods: cone programming, Nesterov-Todd scaling, path-following algorithm, self-dual embedding

Exercises

• Assignment 1.

• Assignment 2. Requires the Matlab file approx_tv_denoising_data.m.

• Assignment 3. Requires the Matlab file l1reglsdata.m.

• Assignment 4. Requires the Matlab file tv_denoising_ex4.m.

• Assignment 5.

• Project assignment (updated on 9/1). Requires the Matlab file project_data.mat.

Technical University of Denmark, June 16–20, 2008

• Lecture 1: Introduction, convex sets, convex functions, modeling software

• Lecture 2: Convex optimization problems, standard problem classes

• Lecture 3: Duality, numerical linear algebra background

• Lecture 4: Unconstrained and equality constrained convex optimization, interior-point methods

• Lecture 5: Examples of convex problems in approximation and fitting, geometry, statistical estimation