Famous theorems that are special cases of linear programming (or convex) duality
Clash Royale CLAN TAG#URR8PPP
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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
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add a comment |
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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
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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.
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– M. Winter
Jan 10 at 21:24
1
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mathoverflow.net/q/252206/12674 looks relevant.
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– Thomas Kalinowski
Jan 11 at 2:04
add a comment |
$begingroup$
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
$endgroup$
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 Jan 10 at 20:06
community wiki
Tom Solberg
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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.
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– M. Winter
Jan 10 at 21:24
1
$begingroup$
mathoverflow.net/q/252206/12674 looks relevant.
$endgroup$
– Thomas Kalinowski
Jan 11 at 2:04
add a comment |
$begingroup$
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.
$endgroup$
– M. Winter
Jan 10 at 21:24
1
$begingroup$
mathoverflow.net/q/252206/12674 looks relevant.
$endgroup$
– Thomas Kalinowski
Jan 11 at 2:04
$begingroup$
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.
$endgroup$
– M. Winter
Jan 10 at 21:24
$begingroup$
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.
$endgroup$
– M. Winter
Jan 10 at 21:24
1
1
$begingroup$
mathoverflow.net/q/252206/12674 looks relevant.
$endgroup$
– Thomas Kalinowski
Jan 11 at 2:04
$begingroup$
mathoverflow.net/q/252206/12674 looks relevant.
$endgroup$
– Thomas Kalinowski
Jan 11 at 2:04
add a comment |
3 Answers
3
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oldest
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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.
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add a comment |
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Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
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add a comment |
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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.
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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 Jan 10 at 23:03
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).
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add a comment |
$begingroup$
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
$endgroup$
add a comment |
$begingroup$
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
$endgroup$
Kőnig's theorem and Hall's marriage theorem are famous and follow from LP duality (together with an integrality argument).
answered Jan 11 at 2:46
community wiki
Thomas Kalinowski
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add a comment |
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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.
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add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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 Jan 11 at 5:43
community wiki
Fedor Petrov
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$begingroup$
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.
$endgroup$
– M. Winter
Jan 10 at 21:24
1
$begingroup$
mathoverflow.net/q/252206/12674 looks relevant.
$endgroup$
– Thomas Kalinowski
Jan 11 at 2:04