I am trying to find the optimal coefficients of the polynomial of the form:
theta=a1*t^2 +a2*t+a3 (i.e., to find a1,a2,a3) for some cost function.
I'm using patternsearch and I need to formulate the nonlinear/linear constraints on a1,a2,a3.
The problem is that I have constraints on theta (say [lb,ub]) and the range of t (say [0,T]), but not on the coefficients themselves.
So far, I've managed to formulate these constraints:
I can't figure out the 3rd constraint on the extrimum on t=-a2/(2*a1). I care only if is in the rectancle [0,T],[lb,ub].