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• W2047510318 abstract "We describe an algorithm to approximate the minimizer of an elliptic functional in the form $int_Omega j(x, u, nabla u)$ on the set ${cal C}$ of convex functions u in an appropriate functional space X. Such problems arise for instance in mathematical economics [4]. A special case gives the convex envelope $u_0^{**}$ of a given function $u_0$ . Let $(T_n)$ be any quasiuniform sequence of meshes whose diameter goes to zero, and $I_n$ the corresponding affine interpolation operators. We prove that the minimizer over ${cal C}$ is the limit of the sequence $(u_n)$ , where $u_n$ minimizes the functional over $I_n({cal C})$ . We give an implementable characterization of $I_n({cal C})$ . Then the finite dimensional problem turns out to be a minimization problem with linear constraints." @default.
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• W2047510318 date "2001-04-01" @default.
• W2047510318 modified "2023-10-01" @default.
• W2047510318 title "A numerical approach to variational problems subject to convexity constraint" @default.
• W2047510318 cites W1653619892 @default.
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• W2047510318 doi "https://doi.org/10.1007/pl00005446" @default.
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