Famous theorems that are special cases of linear programming (or convex) duality
The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization? The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.
oc.optimization-and-control convex-optimization linear-programming
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The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization? The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.
oc.optimization-and-control convex-optimization linear-programming
The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
1
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago
add a comment |
The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization? The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.
oc.optimization-and-control convex-optimization linear-programming
The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any other examples of famous theorems that are also corollaries of LP duality, or duality of convex optimization? The Farkas lemma and the hyperplane separation theorem would be other candidates, although they look more like equivalent statements to me.
oc.optimization-and-control convex-optimization linear-programming
oc.optimization-and-control convex-optimization linear-programming
asked 9 hours ago
community wiki
Tom Solberg
The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
1
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago
add a comment |
The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
1
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago
The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
1
1
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago
add a comment |
3 Answers
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To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
add a comment |
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
add a comment |
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
add a comment |
To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
add a comment |
To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
To elaborate on M. Winter's comment: Von Neumann's minimax theorem for two-person zero-sum games can be thought of as a consequence of LP duality, although his first proof of the theorem did not make this connection explicit.
answered 6 hours ago
community wiki
Timothy Chow
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Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
add a comment |
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
add a comment |
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
answered 3 hours ago
community wiki
Thomas Kalinowski
add a comment |
add a comment |
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
add a comment |
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
add a comment |
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
Bondareva–Shapley_theorem is quite famous in a game theory. In more modern terms, it unites the usual and dual description of the generalized permutohedron.
answered 5 mins ago
community wiki
Fedor Petrov
add a comment |
add a comment |
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The existence of Nash equilibria for matrix games with probabilistic strategies came to my mind, but I don't think there is a famous theorem behind this.
– M. Winter
8 hours ago
1
mathoverflow.net/q/252206/12674 looks relevant.
– Thomas Kalinowski
3 hours ago