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This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems and subsequently...
This work is concerned with the reformulation of evolutionary problems in a
weak form enabling consideration of solutions that may exhibit
evolving microstructures. This reformulation is accomplished by
expressing the evolutionary problem in variational form, i.e., by
identifying a functional whose minimizers represent entire
trajectories of the system. The particular class of functionals under
consideration is derived by first defining a sequence of time-discretized
minimum problems and...
This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...
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