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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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