EXTENSION OF LIPSCHITZ INTEGRANDS AND MINIMIZATION OF
NONCONVEX INTEGRAL FUNCTIONALS APPLICATIONS TO THE
OPTIMAL RECOURSE PROBLEM IN DISCRETE TIME
Abstract: A measurable integrand satisfying a Lipschitz property in on
is extended to the whole of preserving the Lipschitz condition in . This
extension is obtained by using the process developed in [6] for an arbitrary function
Lipschitz on a given subset. The problem of minimizing the integral
over
a subset
of measurable functions
satisfying
almost everywhere is
transformed into the problem of minimizing over
the integral functional
associated with the extended integrand
Comparison results for optimal values as well as
for solutions of the two problems are described. Finally, the results are applied to obtain
necessary conditions for optimality for a class of multistage nonconvex stochastic
programs.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -