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