Necessary conditions for minimum in relaxed variational problems

Necessary Conditions for Solutions to Variational Problems

Ω [F (∇v (x)) + g (x, v (x))] dx with F a convex function defined on RN , it has been conjectured in [2] that the suitable form of the Euler-Lagrange equations satisfied by a solution u should be ∃p(·) ∈ L(Ω), a selection from ∂F (∇u(·)), such that div p(·) = gv(·, u(·)) in the sense of distributions. Equivalently, the condition can be expressed as ∃p(·) ∈ L(Ω) : div p(·) = gv(·, u(·)) and, for...

General necessary conditions for infinite horizon fractional variational problems

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.

Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

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Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

Optimality conditions for nonconvex variational problems relaxed in terms of Young measures

The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler-Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler-Lagrange equation ...