# Tag Info

5

The transformation is mentioned in Ahuja, Magnanti, and Orlin, Network Flows, Exercise 16.25(b).

2

There is a new book Bilevel Optimization Advances and Next Challenges which has a great deal of material on game theory, and how it can be handled with Bilevel Optimization. Chapters: • Interactions Between Bilevel Optimization and Nash Games • On Stackelberg–Nash Equilibria in Bilevel Optimization Games • A Short State of the Art on Multi-Leader-...

1

Is this the formulation that you are looking for: Min-degree constrained minimum spanning tree problem: New formulation via Miller–Tucker–Zemlin constraints Source: http://yoksis.bilkent.edu.tr/pdf/files/10.1016-j.cor.2009.03.006.pdf

19

"General purpose optimization" is quite broad, so I'll take a step back first, to better identifying the motivation of using ML in optimization settings. To keep things simple, I'll consider a single-objective minimization problem with decision vector $x$, objective function $f$ and some constraints $x \in X$, i.e., \begin{align} (P) \ \ \ \min_{x} ...

2

Sometimes it already helps to know the name of a problem. From a more theoretical point of view, i believe that there is a community working on your problem. I know the problem you describe under the term: constraint propagation. For an introduction check for instance: http://www.cs.unibo.it/~gabbri/MaterialeCorsi/CP@CS.pdf

7

Don't know whether this is stating the obvious, but Algorithmic Game Theory by Nisan, Roughgarden, Tardos, and Vazirani has to be in the mix here. Major content would be: (Complexity of) Finding (pure) Nash equilibria, Algorithmic Mechanism Design, the Price of Anarchy (ratio of efficiency between equilibria and optima), Cooperative Games.

3

I'm not sure exactly what you mean by Operations Research framework, but I'll interpret a mathematical treatment, heavy on O.R. and optimization material, as fitting the bill. The book Mathematical Methods and Theory in Games, Programming, and Economics, 1st Edition: Matrix Games, Programming, and Mathematical Economics, by Samuel Karlin was published in ...

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