Linear Programming and Extensions¶
Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Allocation
- This separation — between the universal structural skeleton and the domain-specific criterion that fills it — is what makes allocation portable across substrates that share no institutions, no agents, and no goals, an abstraction Dantzig (1963) pushes furthest in the linear-programming treatment of the transportation problem.
This sourceConsolidated treatment of primal-dual LP including the transportation problem and the simplex method; pushes the abstraction of routing limited supply across sinks furthest. SUPPORTS the claim that Dantzig pushes the allocation abstraction furthest in the LP treatment of the transportation problem.
- This separation — between the universal structural skeleton and the domain-specific criterion that fills it — is what makes allocation portable across substrates that share no institutions, no agents, and no goals, an abstraction Dantzig (1963) pushes furthest in the linear-programming treatment of the transportation problem.
- Minimax Strategy
- The value is computable by linear programming: Player 1's optimal mixed strategy solves $\max v$ subject to $x^\top A \geq v \mathbf{1}$, $x \geq 0$, $\sum x_i = 1$.
This sourceEstablishes the linear-programming formulation and LP duality through which finite zero-sum game values (the maximin optimal mixed strategy) are computed.
- The value is computable by linear programming: Player 1's optimal mixed strategy solves $\max v$ subject to $x^\top A \geq v \mathbf{1}$, $x \geq 0$, $\sum x_i = 1$.
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