The Largest Eigenvalue of a Convex Function, Duality, and a Theorem of Slodkowski

First, we provide an exposition of a theorem due to Slodkowski regarding the largest “eigenvalue” of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for C 2 functions corresponds to the largest eigenvalue of the Hessian. The...

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