CERN Accelerating science

Preprint
Report number	arXiv:1009.1151 ; CERN-PH-TH-2010-199 ; KCL-PH-TH-2010-19 ; MAN-HEP-2010-18 ; CERN-PH-TH-2010-199 ; KCL-PH-TH-2010-19 ; MAN-HEP-2010-18
Title	Note on a Differential-Geometrical Construction of Optimal Directions in Linearly-Constrained Systems
Author(s)	Ellis, John (CERN ; King's Coll. London) ; Lee, Jae Sik (NCTS, Hsinchu) ; Pilaftsis, Apostolos (Manchester U.)
Publication	2010
Imprint	08 Sep 2010
Number of pages	7 p, 7
Note	Comments: 6 pages
Subject category	Mathematical Physics and Mathematics
Abstract	This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat{x}, subject to a system of linear constraints of the form [A] . x = 0, where x is an unknown n-dimensional real vector to be determined up to an overall normalization constant, 0 is an m-dimensional null vector, and the n-dimensional real vector B and the m\times n-dimensional real matrix [A] (with m < n and n >= 2) are given. The analytic solution to this problem can be expressed in terms of a combination of double wedge and Hodge-star products of differential forms.
Other source	Inspire
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