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Concave envelopes of monomial functions over rectangles

✍ Scribed by Harold P. Benson

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
90 KB
Volume
51
Category
Article
ISSN
0894-069X

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✦ Synopsis

Abstract

The construction of convex and concave envelopes of real‐valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

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## Abstract Given a __C__^2^ function __u__, we consider its quasi–convex envelope __u__\* and we investigate the relationship between __D__^2^__u__ and __D__^2^__u__\* (the latter intended in viscosity sense); we obtain two inequalities between the tangential Laplacian of __u__ and __u__\* and the