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Re: Help with Recursive Minimization
*To*: mathgroup at smc.vnet.net
*Subject*: [mg98543] Re: [mg98499] Help with Recursive Minimization
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Sun, 12 Apr 2009 03:47:26 -0400 (EDT)
*References*: <200904110754.DAA22104@smc.vnet.net>
*Reply-to*: drmajorbob at bigfoot.com
The first function is better defined with Set, not SetDelayed:
V1[y_] = First@Minimize[{x/2, x >= 2, x >= y}, {x}]
\[Piecewise] {
{1, y <= 2},
{(y/2), \!\(\*
TagBox["True",
"PiecewiseDefault",
AutoDelete->False,
DeletionWarning->True]\)}
}
Your plot is deceptive, since it leaves out the regions that cause your
third statement to fail. Try this instead:
Plot[V1[y] + 3/y, {y, -5, 5}]
No unconstrained minimum exists, as the plot plainly shows, so this must
fail:
Minimize[V1[y] + 3/y, y]
Minimize::natt: The minimum is not attained at any point satisfying the
given constraints. >>
{-\[Infinity], {y -> 0}}
and so does this:
NMinimize[V1[y] + 3/y, y]
NMinimize::cvdiv: Failed to converge to a solution. The function may be
unbounded. >>
{-2.45422*10^15, {y -> -1.22238*10^-15}}
WITH constraints, however:
Minimize[{V1[y] + 3/y, y > 0}, y]
{Sqrt[6], {y -> Sqrt[6]}}
Bobby
On Sat, 11 Apr 2009 02:54:03 -0500, owen <owenqunwu at hotmail.com> wrote:
> Hi,
>
> I tried to minimize a function which itself is a minimum value
> function. I can plot the function, but cannot get a numerical solution:
>
> V1[y_] := Minimize[{0.5 x, x >= 2, x >= y}, {x}][[1]];
> Plot[ V1[y] + 3/y, {y, 1, 5}]
> Minimize[ V1[y] + 3/y, {y, 1, 5}]
>
> Appreciate your help
> Owen
>
--
DrMajorBob at bigfoot.com
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