Existence and uniform boundedness of optimal solutions of variational problems

Alexander J. Zaslavski

Abstract and Applied Analysis, 1998, vol. 3, 1-28

Abstract:

Given an x 0 ∈ R n we study the infinite horizon problem of minimizing the expression ∫ 0 T f ( t , x ( t ) , x ′ ( t ) ) d t as T grows to infinity where x : [ 0 , ∞ ) → R n satisfies the initial condition x ( 0 ) = x 0 . We analyse the existence and the properties of approximate solutions for every prescribed initial value x 0 . We also establish that for every bounded set E ⊂ R n the C ( [ 0 , T ] ) norms of approximate solutions x : [ 0 , T ] → R n for the minimization problem on an interval [ 0 , T ] with x ( 0 ) , x ( T ) ∈ E are bounded by some constant which does not depend on T .

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:350301

DOI: 10.1155/S1085337598000566

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