Normal vector of a halfspace containing intersections of halfspacesby hwangii Tags: halfspace, halfspaces, intersections, normal, vector 

#1
Nov2112, 10:18 AM

P: 4

Hi all,
does anyone know if there exists a result that proves/disproves the following?: "If a halfspace [itex]\{x \in R^{n}Ax≥0 \}[/itex] for a row vector A contains an finite intersection of halfspaces, [itex]\cap^{m}_{i=1} \{x \in R^{n}A_{i}x \geq 0 \}[/itex], for some row vectors [itex]A_{i}, i=\{1,...,m\}[/itex], then there exists a subset K of {1,...,m} such that [itex]A= \sum_{j \in K} v_{j}A_{j}[/itex] with [itex]v_{j}>0[/itex] for all [itex]j \in K[/itex]" thank you. 


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