# Simple minimization not evaluating

I tried to solve a rather simple optimization problem, which Mathematica apparently cannot handle. A minimal example is the following:

Minimize[{a^2*Exp[-b^2], b > 0}, a, Reals]

(* Minimize[{a^2 E^-b^2, b > 0}, a, Reals] *)


Obviously, the answer should have been {0, {a -> 0}}. The minimization works when I drop the exponential term. My Mathematica version is 10.2.0 for Mac OS X x86 (64-bit) (July 29, 2015).

Are there any options I need to set to aid Mathematica in solving the above minimization or is this simply a bug, which I should report to Wolfram?

• Have a look at NMinimize. – b.gates.you.know.what Aug 4 '15 at 13:48
• Well, I have a more complicated expression with more parameters and I'd like to get the minimum as a function of these parameters. I also believe that the above minimization is simple enough that it could be solved analytically. – David Zwicker Aug 4 '15 at 14:55
• If your expression is non polynomial I don't think Minimize will handle it. – b.gates.you.know.what Aug 4 '15 at 15:06
• I understand that non-linear optimization is hard, but there are a couple of examples in the documentation. Also my optimization problem is polynomial in a, the parameter I optimize for. It would be sufficient if the function realizes that the factor Exp[-b^2] is non-negative. – David Zwicker Aug 4 '15 at 15:13
• If you replace Exp[-b^2] with c, then you get an answer (although if you put in the constraint c > 0, that seems to be ignored). As @b.gatessucks states, Minimize seems to only deal with polynomials and I vaguely remember responses either here or a commmunity.wolfram.com stating so. – JimB Aug 4 '15 at 18:22

Solve[D[a^2*Exp[-b^2], a] == 0, a]