I have a rectangle within a 2d space and a set of points within the rectangle. The rectangle is moving in the following manner: the center moves a value of u on the x-axis, v on the y-axis and everything is scaled in a factor of sx and sy respectively. I only get the location of the points after the motion. My goal is to estimate the (u, v, sx, sy) vector.

I have a function of 4 variables which uses properties of water and steam (iapws library). I also have a group of inequality constraints which too use these properties and bounds for each variable. I want to minimize my function but don’t know the correct way to do so.