# convex hull

(redirected from Convex envelope)
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## convex hull

[′kän‚veks ′həl]
(mathematics)
The smallest convex set containing a given collection of points in a real linear space. Also known as convex linear hull.

## convex hull

(mathematics, graphics)
For a set S in space, the smallest convex set containing S. In the plane, the convex hull can be visualized as the shape assumed by a rubber band that has been stretched around the set S and released to conform as closely as possible to S.
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The vector bundles of each project are first ranked in descending order of their steepest-slope vectors, which are added geometrically to form a convex envelope as shown in Figure 2.
The vector of the convex envelope whose terminal point touches the capital-constraint line has coordinates ([Sigma][Delta]C, [Sigma][Delta]R) whose distance above the 45 [degrees] line through the origin represents the sum [Sigma][Delta]NPV of vectors in the convex envelope, and whose distance along the [Delta]C-axis represents the sum [Sigma][Delta]C of vectors in the convex envelope.
In cases 1 and 2, the vectors first touched by the marginal comparison slope are ranked again in descending order of their slopes and then added geometrically to form a new convex envelope of vectors.
Each vector in the convex envelope represents the best way of doing that project, and vectors that compose the convex envelope up to the capital constraint represent the best projects to do.
The projects are ranked in descending order by capital efficiency or relative profitability, [Delta]R/[Delta]C, to form a convex envelope from which the sequence of best projects are selected.

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