Philon's line generalized: An optimization problem from geometry

Wolfgang Wetterling

doi:10.1007/BF02189793

Philon's line generalized: An optimization problem from geometry

Wolfgang Wetterling

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Consider inn-dimensional Euclidean space the intersection of a convex cone and a hyperplane through a given point. The problem is to minimize the (n-1)-volume of this intersection. A geometric interpretation of the first-order optimality condition is given. The special casen=2 is known as a characteristic property of Philon's line.

Original language	English
Pages (from-to)	517-521
Number of pages	5
Journal	Journal of optimization theory and applications
Volume	90
Issue number	3
DOIs	https://doi.org/10.1007/BF02189793
Publication status	Published - 1996

Keywords

Philon's line
Centroids
Optimality conditions
Convex cones

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10.1007/BF02189793

Wetterling1996philonFinal published version, 200 KB

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Philon's line generalized: An optimization problem from geometry
Wetterling, W., 1995, Enschede: University of Twente. 10 p. (Memorandum; no. 1307)
Research output: Book/Report › Report › Professional

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KW - Philon's line

KW - Centroids

KW - Optimality conditions

KW - Convex cones

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DO - 10.1007/BF02189793

M3 - Article

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SP - 517

EP - 521

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Philon's line generalized: An optimization problem from geometry

Abstract

Keywords

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Philon's line generalized: An optimization problem from geometry

Cite this