The extended Euler-Lagrange condition for nonconvex variational problems

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


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1137/S0363012995283133
ISSNs: 0363-0129 (print)
Related URLs:
Keywords: euler--lagrange condition, calculus of variations, nonconvex differential inclusion, nonsmooth analysis, limiting subdifferential
Subjects: Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29663
Accepted Date and Publication Date:
Date Deposited: 03 May 2007
Last Modified: 31 Mar 2016 11:55

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