Displaying similar documents to “A new series of conjectures and open questions in optimization and matrix analysis”

Lipschitz modulus in convex semi-infinite optimization d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem's data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably...

Weighted energy-dissipation functionals for gradient flows

Alexander Mielke, Ulisse Stefanelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate a global-in-time variational approach to abstract evolution by means of the functionals proposed by Mielke and Ortiz [ (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization. Applications...