Existence and Uniform Boundedness of Optimal Solutions of Variational Problems

@inproceedings{Zaslavski2000ExistenceAU,
title={Existence and Uniform Boundedness of Optimal Solutions of Variational Problems},
author={Alexander J. Zaslavski},
year={2000}
}

Given an x0 ∈ Rn we study the infinite horizon problem of minimizing the expression ∫ T 0 f(t, x(t), x ′(t))dt as T grows to infinity where x : [0, ∞) → Rn satisfies the initial condition x(0) = x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set E ⊂ Rn the C([0, T ]) norms of approximate solutions x : [0, T ] → Rn for the minimization problem on an interval [0, T ] with x(0), x(T ) ∈ E are… CONTINUE READING