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The extended Euler-Lagrange condition for nonconvex variational problems

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This paper provides necessary conditions of optimality for a general variational problem for which the dynamic constraint is a differential inclusion with a possibly nonconvex right side. They take the form of an Euler-Lagrange inclusion involving convexification in only one coordinate, supplemented by the transversality and Weierstrass conditions. It is also shown that for time-invariant, free time problems, the adjoint arc can be chosen so that the Hamiltonian function is constant along the minimizing state arc. The methods used here, based on simple "finite dimensional" nonsmooth calculus, Clarke decoupling, and a rudimentary version of the maximum principle, offer an alternative, and somewhat simpler, derivation of such results to those used by Ioffe and Rockafellar in concurrent research.

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Citation

Vinter, Richard and Zheng, Harry (1997) The extended Euler-Lagrange condition for nonconvex variational problems SIAM Journal on Control and Optimization, 35, (1), pp. 56-77. (doi:10.1137/S0363012995283133).

More information

Published date: 1997
Keywords: euler--lagrange condition, calculus of variations, nonconvex differential inclusion, nonsmooth analysis, limiting subdifferential
Organisations: Operational Research

Identifiers

Local EPrints ID: 29663
URI: http://eprints.soton.ac.uk/id/eprint/29663
PURE UUID: a1629251-0ff7-4123-84e8-311a59e4cb7a

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Date deposited: 03 May 2007
Last modified: 17 Jul 2017 15:57

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Contributors

Author: Richard Vinter
Author: Harry Zheng

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