C2-Lusin approximation of strongly convex functions
C2-Lusin approximation of strongly convex functions
Given a strongly convex function mapping from a Euclidean space to the real one, the authors show that for any \(\varepsilon > 0\), there exists a \(C^2\) strongly convex function that is a Lusin-type approximation of the initial one such that the \(\ell^{\infty}\)-norm of the difference of these functions is less than \(\varepsilon\).
- Massachusetts Institute of Technology United States
Approximation with constraints, Lusin approximation, Convex sets in \(n\) dimensions (including convex hypersurfaces), approximation, Approximation by convex sets, Convexity of real functions of several variables, generalizations, strongly convex function
Approximation with constraints, Lusin approximation, Convex sets in \(n\) dimensions (including convex hypersurfaces), approximation, Approximation by convex sets, Convexity of real functions of several variables, generalizations, strongly convex function
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