Convex optimization

Summary

This course introduces the theory and application of modern convex optimization from an engineering perspective.

Content

Learning Prerequisites

Required courses

Students are assumed to have good knowledge of linear algebra and analysis.

Important concepts to start the course

Some familiarity with linear programming or other optimization paradigms is useful but not necessary. Students are expected to be familiar with PYTHON.

Learning Outcomes

By the end of the course, the student must be able to:

• Model and solve decision problems affected by uncertainty
• Formalize decision problems in engineering and economics as mathematical optimization models
• Solve the resulting models with off-the-shelf optimization software and interpret the results
• Assess / Evaluate the computational complexity of different classes of optimization problems and use modeling techniques to make specific optimization problems more tractable

Transversal skills

• Communicate effectively with professionals from other disciplines.
• Use both general and domain specific IT resources and tools
• Assess one's own level of skill acquisition, and plan their on-going learning goals.
• Write a scientific or technical report.

Teaching methods

Classical formal teaching interlaced with practical exercices and computational courseworks.

Assessment methods

30% Midterm exam

20% Computational projects

50% Final exam

Supervision

Resources

Bibliography

• Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004
• Aharon Ben-Tal and Arkadi Nemirovski, Lectures on Modern Convex Optimization, SIAM, 2001
• Yurii Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2004
• David Luenberger and Yinyu Ye, Linear and Nonlinear Programming, Springer, 2008
• R. Tyrrell Rockafellar, Conjugate Duality and Optimization, SIAM, 1974
• Joshua A. Taylor, Convex Optimization of Power Systems, Cambridge University Press, 2015

Ressources en bibliothèque

• Convex Optimization / Boyd
• Conjugate Duality and Optimization / Rockafellar
• Lectures on Modern Convex Optimization / Ben-Tal
• Linear and Nonlinear Programming / Luenberger
• Introductory Lectures on Convex Optimization: A Basic Course / Nesterov
• Convex Optimization of Power Systems / Taylor

Moodle Link

• https://go.epfl.ch/MGT-418