I have this optimization problem and I am not too sure how to proceed to solve it. So there is a continent y = (x+1)^2 +1 and an island (x^2)+(y^2)=1. We want to build a bridge that links the two functions at points (x1,y1) and (a,b). Here is what the problem is asking for:
a) Formulate a question that consists of minimizing the cost, a problem without constraints of minimization of a degree 4 polynomial with 2 variable x1 and θ, so C(x1,θ) and formulate the conditions of first order.
b) Knowing that the minimum for the cost is reached for
θ=0.562371782 rad and x1=-0.68709
determine the coordinates for the points P1=(x1,y1) and P2=(a,b)