July 4th, 2011, 7:15 am
Following Alan's proposition, here is a short Mathematica code to illustrate the idea (I am not quite sure it is the best place to post this)First define the function that returns your two outputs :(input : t; ouput : x and y)Clear[f];f[t_Real] := Module[{xLocal, yLocal}, xLocal = Sin[t]; yLocal = ArcTan[t]; Return[{xLocal, yLocal}]; ];Then define the one you're really interested in :(input : t; output : x)Clear[g];g[t_Real] := First[f[t]];And minimize the output you care about by 'altering' the input parameter :(is looking for t0, a numerical value of t, such that g is locally minimized;there exists a neighborhood of t0, such that for any t in this neighborhood, g[t] >= g[t0])FindMinimum[g[t], t]You might be interested as well in minimizing the other function, (input t; output y)Clear[g2];g2[t_Real] := Last[f[t]];You will see that Mathematica 8 will give you an answer, although this function is actually problematic, because the solution is intrinsically not bounded. Anyway, Mathematica says something; it is left to you to check, for instance, that the answer is meaningful (I strongly suggest you to do so every time).solution=FindMinimum[g2[t], t];g2[Last[solution][[1, 2]]]Please consider those pieces of Math code carefully. Every problem should be handled properly, and I am not claiming that this represents a universal approach... I only hope it could be a helpful starting point for you.