Nonlinear programming.¶
Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Constraint
- … classical mechanics; Dantzig's 1947 simplex method turned linear constraints into the algorithmic core of operations research, enabling industrial-scale optimization of production, logistics, and resource allocation; Karush's 1939 master's thesis and its 1951 independent rediscovery and extension by Kuhn and Tucker
This sourceEstablishes the Karush–Kuhn–Tucker (KKT) conditions and introduces a vector-maximization formulation with proper efficiency that became the technical foundation for OR-side MOO theory.
- … classical mechanics; Dantzig's 1947 simplex method turned linear constraints into the algorithmic core of operations research, enabling industrial-scale optimization of production, logistics, and resource allocation; Karush's 1939 master's thesis and its 1951 independent rediscovery and extension by Kuhn and Tucker
- Duality
- … cross-side inference: once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual
This sourceEstablishes the Karush–Kuhn–Tucker (KKT) conditions and introduces a vector-maximization formulation with proper efficiency that became the technical foundation for OR-side MOO theory.
- … cross-side inference: once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual
- Multiobjective Optimization
- … codification of MOO as a solution methodology and its primary mature practice location is in OR and adjacent engineering optimization, with the Kuhn–Tucker (1951) nonlinear-programming framework providing the technical scaffolding (KKT conditions, proper efficiency) on which vector-optimization theory was later built.
This sourceEstablishes the Karush–Kuhn–Tucker (KKT) conditions and introduces a vector-maximization formulation with proper efficiency that became the technical foundation for OR-side MOO theory.
- … codification of MOO as a solution methodology and its primary mature practice location is in OR and adjacent engineering optimization, with the Kuhn–Tucker (1951) nonlinear-programming framework providing the technical scaffolding (KKT conditions, proper efficiency) on which vector-optimization theory was later built.
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