Sufficient Conditions in the Calculus of Variations and in the Theory of Optimal Control

Nehari,

doi:10.2307/2039589

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Sufficient Conditions Via Auxiliary Functions1

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2000

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“…Similarly, in the study of sufficient conditions for calculus of variations problems, starting with a solution of the Euler-Lagrange equation, aside the usual methods related to the Jacobi equation (that is the linearized Euler-Lagrange equation), Nehari [21] provides another method using auxiliary functions. In this section we extend his approach to infinite-horizon problems.…”

Section: Sufficient Conditions Via Auxiliary Functionsmentioning

confidence: 99%

Sufficient conditions for infinite-horizon calculus of variations problems

Blot

Hayek

2000

ESAIM: COCV

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Abstract.After a brief survey of the literature about sufficient conditions, we give different sufficient conditions of optimality for infinite-horizon calculus of variations problems in the general (non concave) case. Some sufficient conditions are obtained by extending to the infinite-horizon setting the techniques of extremal fields. Others are obtained in a special case of reduction to finite horizon. The last result uses auxiliary functions. We treat five notions of optimality. Our problems are essentially motivated by macroeconomic optimal growth models.

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Section: Sufficient Conditions Via Auxiliary Functionsmentioning

confidence: 99%