Minimum of explicit functions in vector form

Asked Jan 08 '19 at 15:09

Active Jan 08 '19 at 16:00

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For fun, related to this question about minimizing implicit functions, how can I find the minimum of an explicit one expressed as a vector?

For instance, an ellipse:

orbit[t_] := 
{
   a Cos[2 \[Pi] t/10],
   b Sin[2 \[Pi] t/10]
}

I am finding hard to adapt those solutions for vectors, apart from the obvious solution of minimizing two functions, but I'd like a more elegant vector-like solution if possible, something like

Maximize[{magicHere, orbit[t]}, t]

edited Jan 08 '19 at 16:00

asked Jan 08 '19 at 15:09

senseiwa

This is an explicit (parametrized function from the line to the plane. What is it that needs to be minimized? – Daniel Lichtblau Jan 08 '19 at 15:48
The components of the function (sorry for the wrong characterization, I corrected the question) with respect to t. – senseiwa Jan 08 '19 at 15:59
1

There are two functions, and they have an algebraic dependency. So they cannot be simultaneously minimized. – Daniel Lichtblau Jan 08 '19 at 17:07
So, maybe numerically with NMaximize should do the trick? – senseiwa Jan 10 '19 at 14:58
It remains unclear what is wanted. Without that, I for one cannot suggest what functions to use. – Daniel Lichtblau Jan 10 '19 at 15:57

Minimum of explicit functions in vector form

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