Abstract
We consider a general calculus of variations problem with lower semicontinuous data which includes an optimal control problem with a dynamic differential inclusion constraint as a particular case. We provide a new approach to the derivation of necessary optimality conditions for such a problem, based on a new variant of the multidirectional mean-value inequality for smooth Banach spaces. The multidirectional mean-value inequality is a result in nonlinear and nonsmooth analysis which provides estimates for the minimum difference in function values between a closed convex subset of a Banach space E and a point .
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