Necessary conditions for an extremum in a mathematical programming problem

DOI10.1134/S0081543807010014zbMath1160.49016MaRDI QIDQ2377544

Alexey F. Izmailov, Evgeniy Avakov, Aram V. Arutyunov

Publication date: 19 January 2009

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

concept of 2-regularityfirst-and second-order necessary conditionsminimization problems with equality and inequality constraints

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46) Programming in abstract spaces (90C48) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (13)

On the no-gap second-order optimality conditions for a discrete optimal control problem with mixed constraints ⋮ Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints ⋮ When the Karush-Kuhn-Tucker theorem fails: constraint qualifications and higher-order optimality conditions for degenerate optimization problems ⋮ Necessary and Sufficient Optimality Conditions for Non-regular Problems ⋮ On metric pseudo-(sub)regularity of multifunctions and optimality conditions for degenerated mathematical programs ⋮ Optimality conditions for discrete optimal control problems with equality and inequality type of constraints ⋮ Optimality Conditions for Nonregular Optimal Control Problems and Duality ⋮ Irregular optimization models and \(p\)-order Kuhn-Tucker optimality conditions ⋮ Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints ⋮ Necessary optimality conditions for problems with equality and inequality constraints: Abnormal case ⋮ Generalized convexity in non-regular programming problems with inequality-type constraints ⋮ Lagrange's principle in extremum problems with constraints ⋮ Second-order necessary optimality conditions for a discrete optimal control problem

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• Inverse function theorem and conditions of extremum for abnormal problems with non-closed range
• The Theory of 2-Regularity for Mappings with Lipschitzian Derivatives and its Applications to Optimality Conditions

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