林夏祥 , think again. If we are trying to minimize the maximum distance,
then we want to minimize the upper bound. That is what I specified:
letting c be the upper bound, find the smallest c such that all of the
distances do not exceed c. That gives rise to the inequalities
|x(i)-x(j)| <= c.
If necessary, this can be written as two inequalities:
x(i) - x(j) <= c and
x(j) - x(i) <= c.
Since the relationship is "and," we can just use the two inequalities
as part of the constraint conditions.
Dave
On Oct 21, 12:02 am, 林夏祥 <saltycoo...@gmail.com> wrote:
> I don't think LP can solve it. We are to maximize c, not minimize c.
> The formulas we have are:
>
> |x(i)-x(j)| >= c for all i and j
> r1(i) <= x(i) <= r2(i) for all i
> The first inequality actually is combination of two linear equalities: x(i)
> - x(j) >= c or x(i) - x(j) <= -c. Notice the relation of the two is "or",
> and we cannot put them together to get a system of linear inequalities.
> 2009/10/21 Dave <dave_and_da...@juno.com>
>
>
>
>
>
>
>
> > This is a linear programming problem. The way you formulate the
> > problem depends on the capabilities of the linear programming software
> > you have.
>
> > Basically, you want to
> > minimize c
> > by finding x(1) to x(n) such that
>
> > |x(i)-x(j)| <= c for all i and j
> > r1(i) <= x(i) <= r2(i) for all i
>
> > Dave
>
> > On Oct 5, 9:22 am, monty 1987 <1986mo...@gmail.com> wrote:
> > > We have to locate n points on the x-axis
> > > For each point xi
> > > the x co-ordinate of it lies between a range
> > > [r1i,r2i]
> > > Now we have to decide the location of points such that
> > > minimum { distance between any two points } is maximum.
>
> > > Any answer is welcomed.
>
> --
> 此致
> 敬礼！
>
> 林夏祥- Hide quoted text -
>
> - Show quoted text -
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