I am working on an optimization problem but ran into a problem.
Here is a simplified version of the problem:
foo1a[t_] := {Cos[t], Sin[t]}
foo1b[t_] := {Cos[t], -Sin[t]}
foo1[a_] :=
NMaxValue[{t + EuclideanDistance[foo1a[t], foo1b[t]] - a,
a <= t <= 2 a}, t]
foo2a[t_] := {-Cos[t], Sin[t]}
foo2b[t_] := {-Cos[t], -Sin[t]}
foo2[a_] :=
NMaxValue[{t + EuclideanDistance[foo2a[t], foo2b[t]]*(0.5 + a),
a <= t <= 2 a}, t]
NMinimize[Max[foo1[a], foo2[a]], a]
So I want to minimize the max value of several functions, which return the max value of a function over a given interval. The problem is that the interval depends on the parameters but mathematica wants me to have fixed parameters (Returns error: NMaxValue: The following constraints are not valid: {a<=t,t<=2 a}. Constraints should be equalities, inequalities, or domain specifications involving the variables.).
Is there any way to solve this or could another approach circumvent this problem?