Lecture 9: Benders’ decomposition: Theory

Course: Advanced Optimization and Game Theory for Energy Systems
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.
Lecturer: Jalal Kazempour (Technical University of Denmark, DTU)
Slides are available at: www.jalalkazem...
Course description: kurser.dtu.dk/...
Course content (all video lectures are available in this channel):
Course introduction
Lecture 1: Market clearing as an optimization problem
Lecture 2: Market clearing as an equilibrium problem
Lecture 3: Desirable properties of market-clearing mechanisms
Lecture 4: Market clearing using a cooperative game approach
Lecture 5: Stochastic market clearing
Lecture 6: Robust approaches for market clearing
Lecture 7: Bilevel programming in energy systems
Lecture 8: Optimization problems with decomposable structure
Lecture 9: Benders’ decomposition: Theory
Lecture 10a: Benders’ decomposition: Applications
Lecture 10b: Nested Benders’ decomposition
Lecture 11: Augmented Lagrangian relaxation
Lecture 12: Variants of ADMM and applications

[@derinncagan]

The best explanation so far for the bender's decomposition yet in KZbin. Thanks a lot!

[@JZL003]

This is truly an amazing set of lectures. I've been trying to understand benders decomp and nothing has come even half as close. I am very thankful

[@JiayuWang-d6g]

So clear! Provide intuition through diagrams and now I fully understand what Benders Decomposition is doing! Thank you so much!

[@naghipakdaman]

I would say that I finally found out how BD works. Very excellent teaching

[@大黄老鼠皮卡丘]

It is so clear and I can figure out what is Benders decomposition through this video! Thanks so much!!!

[@lucibeck4352]

Dear Jalal, Thank you for sharing these fruitful lectures with us.

[@sandeepayyagari]

I should thank the attendees since they have asked most of the questions which I do have. Also, thank you, prof. Jalal wonderful demonstration.

[@mrweisu]

Thanks for the lecture! But I hope you have given more details on feasibility cuts. If some of the variables are binary, adding slack is not intuitive

[@josemanuelslatercarrasco617]

Thanks for the video. Does anyone know how to prove equivalence of the x = x_fixed trick for the compact form benders cut alternative? Struggling with KKT.

[@huybui986]

Hi, thank you for sharing but can you explain what's dual variable and how we calculator it ?

[@supakarnsompasong4813]

Thank you for this explanation video. Sir, I have some questions. Does Benders Decomposition can handle equality constraints or I have to use another decomposition method?

[@lucibeck4352]

I have a suggestion: as many students struggle with coding part, is it possible to upload the exercise (python) codes any where?

[@RajuDas-sj8gg]

Can u explain how evaluate dual variable... Plz..🙏

[@shaileshwasti407]

Can you write more about which dual variable you didn't understand in the formulation?

[@ggPescesgg]

Its a great instructive video, thank you so much. However, as a constructive input, I think its misleading to write "Theory" in the title if you are explaining Benders only on example and applications, and not actually deriving the mathematical grounds of the method.

[@yuanxiwu9451]

Dear Jalal, I think for compact form, the sign of dual variable rou also matters. In your slides, I think rou is corresponding to x(fixed)-x(i)=0, not x(i)-x(fixed)=0. Am I right?