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On convexity proofs in location theory

✍ Scribed by Robert F. Love; James G. Morris

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 131 KB
Volume: 25
Category: Article
ISSN: 0894-069X
DOI: 10.1002/nav.3800250115

No coin nor oath required. For personal study only.

✦ Synopsis

It is often assumed in the facility location literature that functions of the type +i(z, y) =p,{(zj-z)*+ (yi-y)a]R/s are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given. DIFFERENTIABILITY Consider one component of t$(z, y) denoted by t$,(s, y), given as +l(z, y)=[(s,-z)*+(yfy)qR/*. (We let B j = l with no loss of generality for the purpose at hand.) A direction in E* is given

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