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p-th Order Optimality Conditions for Singular Lagrange Problem in Calculus of Variations. Elements of p-Regularity Theory

Abstract : This paper is devoted to singular calculus of variations problems with constraints which are not regular mappings at the solution point, e.i. its derivatives are not surjective. We pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we present necessary conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.
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Agnieszka Prusińska, Ewa Szczepanik, Alexey Tret’yakov. p-th Order Optimality Conditions for Singular Lagrange Problem in Calculus of Variations. Elements of p-Regularity Theory. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.528-537, ⟨10.1007/978-3-642-36062-6_53⟩. ⟨hal-01347581⟩

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