A duality-based approach to elliptic control problems in non-reflexive Banach spaces
Christian Clason, Karl Kunisch (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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Convex duality is a powerful framework for solving non-smooth optimal control problems. However, for problems set in non-reflexive Banach spaces such as L(Ω) or BV(Ω), the dual problem is formulated in a space which has difficult measure theoretic structure. The predual problem, on the other hand, can be formulated in a Hilbert space and entails the minimization of a smooth functional with box constraints, for which efficient numerical methods exist. In this work, elliptic control...