Convex Optimization, Spring 2017

Last modified by asaekman@helsinki_fi on 2024/03/27 10:29

Convex Optimization, Spring 2017

 

Teacher: Martin S. Andersen (contact person Åsa Hirvonen)

Scope: 2 cr

Type: Advanced

Teaching: Lectures and exercises each day during the course

Topics:

Prerequisites: Coursework in linear algebra and familiarity with a high-level programming language such as MATLAB, Python, or Julia.

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News

  •  This is a minicourse with lectures and exercises each day. Do bring your own laptop if you have one (you can work in groups if you don't have one).

Teaching schedule

9.-13.1.2017 in D122

Monday-Thursday 9-16.30, Friday 9-15

Course contents

The course gives an introduction to convex optimization with a focus on large-scale optimization. The topics will include:

  • 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 (proximal gradient methods, acceleration)
  • Splitting methods (operator splitting, Douglas–Rachford splitting, ADMM, Chambolle–Pock algorithm)
  • Incremental methods and coordinate descent methods
  • Derivative-free optimization

Exams

There is no exam, the course is evaluated based on exercises and course activity.

Course material

Texts:

• S. Boyd and L. Vandenberghe: “Convex Optimization”, Cambridge University Press, 2003. Available here.

• A. Ben-Tal and A. Nemirovski: “Lectures on Modern Convex Optimization”, lecture notes, 2013. Available here.

Other resources:

• S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein: “Distributed optimization and statistical learning via the alternating direction method of multipliers”, Foundations and Trends in Machine Learning, 3(1):1–122, 2011. Available here.

• N. Parikh and S. Boyd: “Proximal Algorithms”, Foundations and Trends in Optimization, 1(3):123-231, 2014. Available here.

• E. K. Ryu and S. Boyd: “Primer on Monotone Operator Methods”, Appl. Comput. Math., 15(1):3-43, 2016. Available here.

• A. Beck & M. Teboulle: “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems”, SIAM J. Imaging Sci., 2(1), 183–202, 2009. Available here.

Registration


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Exercises

 

Course feedback

Course feedback can be given at any point during the course. Click here.