Re: Minimum distance from a point to a surface defined by constraints

From: carkaci (carkaci_at_yahoo.com)
Date: 03/03/05 

Date: 3 Mar 2005 06:46:18 -0800

astanoff@yahoo.fr wrote:
> Numerically, you can do it this way, with mathematica (3D example) :
>
> pointP = {2,3,4};
>
> pointX = {x,y,z};
>
> distance = Sqrt[(pointP-pointX).(pointP-pointX)];
>
> constraints = x+y+z <= 1 && x+2y+z <= 2;
>
> NMinimize[{distance, constraints}, pointX]
>
> {4.6188, {x -> -0.666667, y -> 0.333333, z -> 1.33333}}

I think, you clearly understand what i mean. However, I wonder the
algorithm. Is there a faster way to compute the minimum distance ? I
suppose, it can be solved much simpler and more fast than any other
Optimization problems. Of course, I hope so. Because, the constraints
are normalized.

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