An elementary proof of the Karush–Kuhn–Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints

DOI10.1080/02331930903552473zbMath1222.90080OpenAlexW2044758295MaRDI QIDQ3093086

Olga A. Brezhneva, Alexey A. Tret'yakov

Publication date: 12 October 2011

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930903552473

zbMATH Keywords

optimality conditionslinear independenceconstraint qualificationsinequality-constrained optimizationKarush-Kuhn-Tucker theorem

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46)

Related Items (7)

A sharp Lagrange multiplier theorem for nonlinear programs ⋮ Nonlinear programming via König's maximum theorem ⋮ New perspective on some classical results in analysis and optimization ⋮ New perspective on the Kuhn-Tucker theorem ⋮ A new proof of the Kuhn-Tucker and Farkas theorems ⋮ Revisiting the Hahn-Banach theorem and nonlinear infinite programming ⋮ An elementary proof of the Lagrange multiplier theorem in normed linear spaces

Cites Work

• A simple and elementary proof of the Karush-Kuhn-Tucker theorem for inequality-constrained optimization
• Optimization in Banach spaces
• Optimality conditions and constraint qualifications in Banach space
• Optimization theory in linear spaces. III: Mathematical programming in partially ordered Banach spaces
• Duality for Nonlinear Programming in a Banach Space
• A Necessary and Sufficient Qualification for Constrained Optimization

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