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In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
Las condiciones de Karush-Kuhn-Tucker (también conocidas como las condiciones KKT o Kuhn-Tucker) son requerimientos necesarios y suficientes para que la solución de un problema de programación matemática sea óptima. Es una generalización del método de los multiplicadores de Lagrange.
3 de may. de 2016 · A triple satisfying the KKT optimality conditions is sometimes called a KKT-triple. This generalizes the familiar Lagrange multipliers rule to the case where there are also inequality constraints. The result was obtained independently by Karush in 1939, by F. John in 1948, and by H.W. Kuhn and J.W. Tucker in 1951, see [1] , [7] .
William Karush (1 March 1917 – 22 February 1997) was an American professor of mathematics at California State University at Northridge and was a mathematician best known for his contribution to Karush–Kuhn–Tucker conditions.
- March 1, 1917, Chicago, IL
- Contribution to Karush–Kuhn–Tucker conditions
2 KKT Conditions TheKarush-Kuhn-Tucker(KKT)conditionsareageneralizationofLagrangemultipliers,andgiveasetofnecessary conditionsforoptimalityforsystemsinvolvingbothequalityandinequalityconstraints.
29 de sept. de 2020 · Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization. Published: 29 September 2020. Volume 187 , pages 469–487, ( 2020 ) Cite this article. Download PDF. Journal of Optimization Theory and Applications Aims and scope Submit manuscript. Gabriel Haeser & Alberto Ramos. 824 Accesses. 7 Citations.
The KKT conditions are. 1. Lagrangian function definition: L = ( x − 10) 2 + ( y −8) 2 + u1 ( x + y −12) + u2 ( x − 8) 2. Gradient condition: (a) 3. Feasibility check: (b) 4. Switching conditions: (c) 5. Nonnegativity of Lagrange multipliers: u1, u2 = 0. 6. Regularity check. View chapter Explore book.