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• W2271489623 abstract "In this paper we address the problem of identifying those functions whose convex envelope on a polyhedron P coincides with the convex envelope of their restrictions to the vertices of P. When this property holds we say that the function has a vertex polyhedral convex envelope. The interest for identifying this property is due to the fact that if a function has a vertex polyhedral convex envelope on P, then such convex envelope can be computed exactly in finite time and it can be expressed as the maximum of a finite family of affine functions. This implies that the minimum of the convex envelope on P can be obtained by means of a linear program. The main results of this paper are the facts that a function f has a vertex polyhedral convex envelope on P if and only if for every affine function g, the modified function f (x) + g (x) attains its minimum at a vertex of P and that this property holds if f is edge concave on P,i.e., concave along all directions parallel to an edge of P. We also show that edge concavity of f on P holds for all classes of functions previously known to admit a vertex polyhedral convex envelope and we describe some new classes of functions for which the existence of a vertex polyhedral convex envelope is guaranteed." @default.
• W2271489623 created "2016-06-24" @default.
• W2271489623 creator A5049469173 @default.
• W2271489623 date "2004-01-01" @default.
• W2271489623 modified "2023-09-25" @default.
• W2271489623 title "On the existence of polyhedral convex envelopes" @default.
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• W2271489623 doi "https://doi.org/10.1007/978-1-4613-0251-3_30" @default.
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