# Find the max/min of some function given multiple parameters?

GROUPS:
 Say I have a simple function and I want to find its minimum for different parameters (an optimization problem), how do I do that? http://puu.sh/Adkbi/04dbda4dd3.png This for instance, I don't care about complex roots I want it to show all reals, how to do that? http://puu.sh/AdkcI/5710a78156.png doing it this way says the constraints are wrong even though they are inequalities? If there is a way to make a Hesse's matrix that would work too. This is how it could look like for instance for some a,b,c,d,f > 0 http://puu.sh/AdkeR/a00f325581.png . Now I don't want to plot it, I just want to see the optimums for say 50=>a>=1 etc.Thanks in advance.
26 days ago
4 Replies
 For simple problems Maximize and Minimize can symbolically handle problems with parameters. Here's an example from the documentation In[1]:= Maximize[a x^2 + b x + c, x] Out[1]= {\[Piecewise] { {c, (b == 0 && a == 0) || (b == 0 && a < 0)}, {-((b^2 - 4 a c)/(4 a)), (b > 0 && a < 0) || (b < 0 && a < 0)}, {\[Infinity], \!$$TagBox["True", "PiecewiseDefault", AutoDelete->False, DeletionWarning->True]$$} }, {x -> \[Piecewise] { {0, (b == 0 && a == 0) || (b == 0 && a < 0)}, {-(b/(2 a)), (b > 0 && a < 0) || (b < 0 && a < 0)}, {Indeterminate, \!$$TagBox["True", "PiecewiseDefault", AutoDelete->False, DeletionWarning->True]$$} }}} 
 NMinimize[{(5 + x^3.5)/x, x > 0}, x] (* Out: {5.742347492053465,{x\[Rule]1.2190136481282579}} *) For negative arguments your function becomes complex valued, so this should be excluded from the search. And the respective constrains refer to the argument and not to any parameters.