Guy Bouchitté, Ilaria Fragalà
Published 2016-07-11Version 1
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in \cite{BoFr}.
A duality theory for some non-convex functions of matrices
Periodic Hamiltonian systems in shape optimization problems with Neumann boundary conditions
A primal dual variational formulation suitable for a large class of non-convex problems in optimization
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