Abstract
Quasiconvex (QC) functions are functions whose level sets are convex. The quasiconvex envelope (QCE) of a given function, g, is the maximal QC function below g. The QCE provides a level set representation for the convex hull of every level set of a given function. We present a nonlocal line solver for computing the QCE of a given function. The algorithm is based on solving the one dimensional problem on lines, which can be done by a fast marching or sweeping method. Convergence of the algorithm is established.
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Abbasi, B., Oberman, A.M. Computing the Level Set Convex Hull. J Sci Comput 75, 26–42 (2018). https://doi.org/10.1007/s10915-017-0522-8
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DOI: https://doi.org/10.1007/s10915-017-0522-8
Keywords
- Convexity
- Level set method
- Quasiconvexity
- Partial differential equation
- Generalized convex envelopes
- Finite difference method
- Viscosity solutions