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Lecture 11: Augmented Lagrangian relaxation

Jalal Kazempour

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Course: Advanced Optimization and Game Theory for Energy Systems
Lecturer: Jalal Kazempour (Technical University of Denmark, DTU)

This is an online intense PhD-level course that took place during the first 3 weeks of January 2021 with 120 students from all over the world.

Slides are available at: https://www.jalalkazempour.com/teaching
Course description: https://kurser.dtu.dk/course/2022-202...

Course content:
Course introduction (Course introduction)
Lecture 1: Market clearing as an optimization problem (Lecture 1: Market clearing as an optimizat...)
Lecture 2: Market clearing as an equilibrium problem (Lecture 2: Market clearing as an equilibri...)
Lecture 3: Desirable properties of market-clearing mechanisms (Lecture 3: Desirable properties of market-...)
Lecture 4: Market clearing using a cooperative game approach (Lecture 4: Market clearing using a coopera...)
Lecture 5: Stochastic market clearing (Lecture 5: Stochastic market clearing)
Lecture 6: Robust approaches for market clearing (Lecture 6: Robust approaches for market cl...)
Lecture 7: Bilevel programming in energy systems (Lecture 7: Bilevel programming in energy s...)
Lecture 8: Optimization problems with decomposable structure (Lecture 8: Optimization problems with deco...)
Lecture 9: Benders’ decomposition: Theory (Lecture 9: Benders’ decomposition: Theory)
Lecture 10a: Benders’ decomposition: Applications (Lecture 10a: Benders’ decomposition: Appli...)
Lecture 10b: Nested Benders’ decomposition (Lecture 10b: Nested Benders’ decomposition)
Lecture 11: Augmented Lagrangian relaxation (Lecture 11: Augmented Lagrangian relaxation)
Lecture 12: Variants of ADMM and applications (Lecture 12: Variants of ADMM and applications)

3 Comments

@amirzare6172 3 years ago

Thanks a lot, professor, that's very practical.

@lahlouaziz695 4 years ago (edited)

I have a question : what if we have to optimize a cost (with a monetary unit) as an objective function and the constraint has a different unit, how to deal with this ? I mean the relaxed problem in its objective function will have a term with a monetary unit while the other term with the dual variable will have a different unit. Please correct me if I am wrong

@yingkaisong4258 4 years ago

I do not quite understand why the standard LR needs the quadratic assumption. From what was illustrated in the slides, it is not obvious why a linear obj cannot work. Also, I am confused a bit about the logic here: the standard LR needs contiuously differentiable --> thus, the obj needs to be quadratic --> thus linear obj cannot work. Firstly, not only quadratic functions are continuously differentiable; secondly, linear functions are surely continuously differentiable.