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In this work, we improve the approach of [15] to nonlinear error bounds for lower semicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and allows dealing with local error bounds in an appropriate way. We present(More)
In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. The constraint set being defined by C = g−1(K) where g is a smooth map between Banach spaces, and K a closed convex cone, we show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to metric subregularity of the(More)
To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some(More)
  • D. Azé
  • Foundations of Computational Mathematics
  • 2009
The topic of this monograph ranges beyond its title. We are in presence of a volume which gives a large survey of calculus of variations in several variables with detours into partial differential equations of variational type, but also captures some parts of mathematical programming and convex analysis. It is destined for graduate and postgraduate(More)
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