Duality: constraint relaxation

Bierlaire (2015) Optimization: principles and algorithms, EPFL Press. Section 4.1

[@albertelinello]

Dear Professor, in 14 minutes you won m as a student! Thank you for your explanation and the sharing! Masterclass!!!

[@suminoh2869]

Thank you for such a simplified, digestible explanation of the concept!

[@Darkdivh]

Dear professor Bierlaire, thank you for the clarification. It helps me to understand principles of User Equilibrium modelling in Traffic Assignment, merci

[@gobichai2704]

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[@yiranchang136]

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[@ahmedelsabagh6990]

Great explanation, Thanks for your efforts

[@oussemamhiri9713]

Great explanation!

[@QinyuChen]

Amazing vedio, my English not very well, but still can get ur meaning quickly.

[@fabianleuthold2502]

Great explanation! Thanx a lot! One question: If we were solving the dropped equality constraint - equation by x2 = 1 - x1 and replaced x2 in the objective function by (1 - x1) directly, we would find the new objective function without having to introduce and find a correct value for lambda. Is this always possible when we're trying to relax equality-constraints or could that go wrong?

[@MichelBierlaire]

The discussion in the video is about deriving the dual of a given model formulation. What you suggest is to change the formulation, to use the equality constraints to eliminate some variables from the formulation. In your example, what can go wrong is that 1-x1 becomes negative. So you need to keep track of the original variables. This is exactly what the simplex algorithm is doing.

[@benjaminbenjamin8834]

Awesome!

[@ShamsBasir]

2-x2 would be minimized if we set x2 = infinity which is satisfying the other constraints as well and it is unbounded. How did we get the optimal solution as -infinity < 1 . thanks

[@benjaminbenjamin8834]

Respected Professor please make some videos on convex optimization tutorial with examples related to machine learning algorithms ,like SVM, GANs etc

[@imadeddineaziez7585]

Thank you !