Variational Calculus with Elementary Convexity

By J. Troutman. 1983

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Proper local scoring rules (2011, methodology): “To address this problem we adopt the methods of variational calculus [Troutman (1983), van Brunt (2004)].”
Regularized derivatives of potential fields and their role in semi‐automated interpretation methods (2009, unknown): “We use the known Euler-Lagrange equation from the variational calculus theory (e.g., Bath 1968; Troutman 1983) to find an extreme of the variational problem: d dx ( ∂F ∂ f ′ ) − ∂F ∂ f = 0, where we use: ∂F ∂ f ′ = 2α f ′ (x) , d dx ( ∂F ∂ f ′ ) = 2α f ′′ (x) , ∂F ∂ f = 2 [ f (x) − A(Uδ)] , and we…”
Asymptotic L1-decay of solutions of the porous medium equation to self-similarity (2000, methodology): “To prove this, considering that H(uju1) is convex in u, we can make use of the usual variational argument with Lagrange multipliers [20].”