A high-order generalization of the Lyusternik theorem

DOI10.1016/S0362-546X(98)00001-7zbMath0954.49014MaRDI QIDQ4264243

Heinz Schättler, Urszula Łedzewicz-Kowalewska

Publication date: 8 February 2001

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

level setextremum problemstangent setopen mapping principleLyusternik theorem

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimality conditions for problems involving ordinary differential equations (49K15) Optimality conditions for problems in abstract spaces (49K27) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

Related Items (8)

Degenerate equality constrained optimization problems and P-regularity theory ⋮ Optimization and flow invariance via first and second order tangent cones ⋮ Higher-Order Optimality Conditions and Higher-Order Tangent Sets ⋮ Third order open mapping theorems and applications to the end-point map ⋮ \(p\)-regular nonlinearity: tangency at singularity in degenerate optimization problems ⋮ Implicit function and tangent cone theorems for singular inclusions and applications to nonlinear programming ⋮ Generalized implicit function theorem and its application to parametric optimal control problems ⋮ Come Back to Lagrange. Thep-Factor Analysis of Optimality Conditions

Cites Work

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• Some inverse mapping theorems
• Necessary extremum conditions for smooth anormal problems with equality- and inequality-type constraints
• Necessary conditions for a minimum for nonregular problems in Banach spaces. A maximum principle for abnormal optimal control problems
• An open mapping principle for set-valued maps
• Higher order necessary conditions in abstract mathematical programming
• Extension of the local maximum principle to abnormal optimal control problems
• Second-order conditions for extremum problems with nonregular equality constraints
• On abnormal optimal control problems with mixed equality and inequality constraints
• Lectures on mathematical theory of extremum problems. Translated from the Russian by D. Louvish
• Some mapping theorems
• Extremum conditions for smooth problems with equality-type constraints
• On the local surjection property
• LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA
• Second-order conditions in extremal problems. The abnormal points
• High-Order Approximations and Generalized Necessary Conditions for Optimality
• Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions
• On the Lusternik theorem for nonsmooth operators
• An Inverse Mapping Theorem for Set-Valued Maps
• AN EXTENDED MAXIMUM PRINCIPLE
• QUADRATIC CONDITIONS FOR A PONTRYAGIN MINIMUM IN AN OPTIMAL CONTROL PROBLEM LINEAR IN THE CONTROL. II. THEOREMS ON WEAKENING EQUALITY CONSTRAINTS
• Set-valued analysis

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