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Optimal Lp-Approximation of a Convex Set by a Convex Subset

Solve the shape-optimization problem of choosing, inside a fixed convex container, a convex subset of prescribed measure that best approximates the container in the Lp sense, minimizing the p-distance between their support functions. Establish existence of optimal shapes, analyze the limit behavior as p grows, characterize the geometry of the optimal boundary, and design a numerical scheme that captures straight boundary segments.

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Lp Convex-Subset Approximations Gamma-Converge to the Hausdorff Problem with Polygonal Free

A shape-optimization research paper in the calculus of variations. Given a fixed convex container in n-dimensional Euclidean space, it studies how to choose a convex subset of prescribed measure that…