Re: [R] The smallest enclosing ball problem

2013-11-17 Thread Hans W.Borchers
Berend Hasselman xs4all.nl> writes: > It seems you are absolutely right. I always assumed a quadratic programming solver will -- as all linear programming solvers do -- automatically require the variables to be positive. I checked it for some more examples in 10 and even 100 dimensions, and t

Re: [R] The smallest enclosing ball problem

2013-11-17 Thread Berend Hasselman
On 17-11-2013, at 11:32, Hans W.Borchers wrote: > Berend Hasselman xs4all.nl> writes: >> Forgot to forward my answer to R-help. >> >> Berend > > Thanks, Berend, for thinking about it. \sum xi = 1 is a necessary condition > to generate a valid geometric solution. The three points in the exam

Re: [R] The smallest enclosing ball problem

2013-11-17 Thread Hans W.Borchers
Berend Hasselman xs4all.nl> writes: > Forgot to forward my answer to R-help. > > Berend Thanks, Berend, for thinking about it. \sum xi = 1 is a necessary condition to generate a valid geometric solution. The three points in the example are very regular and your apporach works, but imagine som

Re: [R] The smallest enclosing ball problem

2013-11-17 Thread Berend Hasselman
On 16-11-2013, at 13:11, Hans W.Borchers wrote: > I wanted to solve the following geometric optimization problem, sometimes > called the "enclosing ball problem": > >Given a set P = {p_1, ..., p_n} of n points in R^d, find a point p_0 such >that max ||p_i - p_0|| is minimized. > > A

Re: [R] The smallest enclosing ball problem

2013-11-16 Thread Berend Hasselman
Forgot to forward my answer to R-help. Berend On 16-11-2013, at 13:11, Hans W.Borchers wrote: > I wanted to solve the following geometric optimization problem, sometimes > called the "enclosing ball problem": > > Given a set P = {p_1, ..., p_n} of n points in R^d, find a point p_0 such >

[R] The smallest enclosing ball problem

2013-11-16 Thread Hans W.Borchers
I wanted to solve the following geometric optimization problem, sometimes called the "enclosing ball problem": Given a set P = {p_1, ..., p_n} of n points in R^d, find a point p_0 such that max ||p_i - p_0|| is minimized. A known algorithm to solve this as a Qudratic Programming task is