New answers tagged reference-request
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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