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


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-...


Is this the formulation that you are looking for: Min-degree constrained minimum spanning tree problem: New formulation via Miller–Tucker–Zemlin constraints Source:


"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} ...


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:


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.


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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