Forrest Laine

Dad mode

[Forrest Laine @4estLaine]

@VoteJ50082 @freddieoconnell @MetroSchools Parody accounts are supposed to actually be funny

[Forrest Laine @4estLaine]

@elonmusk Fuck you dude have a higher standard

[Forrest Laine @4estLaine]

@UrbanEastNash Flashing yield signs where Dickerson and 1st street merge

[Forrest Laine @4estLaine]

I also developed a Julia package for modeling and solving QPNs, using the algorithms derived in the paper. It's not perfect. There are limitations in the type of QPN that can be solved.

Try it out--if your problem stumps the algorithm, let me know!

https://t.co/ZCc685khwa

[Forrest Laine @4estLaine]

The results were fascinating. Here are 6 of the 47 possible configurations, with the relative cost advantage over the Nash configuration shown for the node in yellow. I used to believe that leading was always preferable to following. This is evidently not always the case!

[Forrest Laine @4estLaine]

@ylecun 8MB is a huge amount of information. That can encode one of 2^64mil configurations. There are only 2^256 or so atoms in the universe.

[Forrest Laine @4estLaine]

@beenwrekt I’d argue game theory should be below and to right of MPC. You can formulate MPC as a simple type of game. Therefore GT has to be at least as impactful as MPC. A less simple game formulation could be more impactful but will be slower to solve than MPC.

[Forrest Laine @4estLaine]

Lesson 1:

https://t.co/5cI3eCoRYE

[Forrest Laine @4estLaine]

Lesson 1, equating optimizers of MPs to KKT points.

Consider a convex MP with a polyhedral feasible region. We will prove the following.

[Forrest Laine @4estLaine]

I've decided I will try to post some material from my class this semester, Extended Mathematical Programming.

[Forrest Laine @4estLaine]

This class covers some theory and algorithms pertaining to classic examples of Extended Mathematical Programming problems. I will try to post as much content here as I can keep up with!

[Forrest Laine @4estLaine]

Finally, we can remove the dependence on the active set J by leveraging the notion of complementarity. For all non-active constraints, the corresponding elements of lambda must be 0. The equivalence of these two expressions follows, finally proving the result.

[Forrest Laine @4estLaine]

Lesson 1, equating optimizers of MPs to KKT points.

Consider a convex MP with a polyhedral feasible region. We will prove the following.

[Forrest Laine @4estLaine]

Having derived this equivalent definition of optimality, we can use Farka's Lemma to transform our expression once more.