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Convex optimization


Technical University of Denmark


General course objectives:
The aim of the course is to provide students with a general overview of convex optimization theory, its applications, and computational methods for large-scale optimization. The students will learn how to recognize convex optimization problems and how to solve these numerically using either an existing software library or by deriving/implementing a suitable method that exploits problem structure. As part of the course, the students will work on a project which aims to provide students with the opportunity to put theory to work in a practical and application-oriented context.

Learning objectives:
A student who has met the objectives of the course will be able to:
  • recognize and characterize convex functions and sets
  • explain/characterize the subdifferential of a convex function
  • describe basic concepts of convex analysis
  • derive the Lagrange dual of a convex optimization problem
  • recognize and formulate conic constraints
  • derive a convex relaxation of nonconvex quadratic problems
  • implement a first-order method for a large-scale optimization problem with structure
  • construct and implement a splitting method for a convex–concave saddle-point problem
  • evaluate the computational performance of an optimization algorithm

Contents:
Convex analysis (convex sets and functions, convex conjugate, duality, dual norms, composition rules, subgradient calculus), conic optimization (linear optimization, second-order cone optimization, semidefinite optimization), first-order methods for smooth and nonsmooth optimization (proximal gradient methods, acceleration), splitting methods (Douglas–Rachford splitting, ADMM, Chambolle–Pock algorithm), stochastic methods, incremental methods and coordinate descent methods.

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Course organizer
Martin Skovgaard
Place/Venue
Anker Engelunds Vej 1
City
2800 Kgs. Lyngby
Country
Denmark
Workload
5
Link
http://kurser.dtu.dk/course/02953