So I have a problem where three points are situated on a vertical line. There is a fourth point projecting out from the line that I do not know the coordinates of. The three points all estimate a given line connecting itself with the fourth point. These lines are represented by angles created by the estimated line and the line normal to the horizontal line. Here is the best graphical representation I can draw.
y is the point I am trying to figure out the coordinates of. a, b, and c are all three points I know the coordinates of (and are always on the same vertical line). The three angles are measured from the dashed line to the lines created by the backward and foreword slashes. You should disregard the dots. They are there because the spaces I had in their place got deleted upon submitting the thread. Note these angles are just estimates and do not intersect at point y. For instance, the angle associated with b could be pi/16 or something close to 0. So a, b, and c can be represented as y(1), y(2), and y(3) and then the angles can be represented as o(1), o(2), and o(3). I need to pick three angles (lets call them p(1), p(2), and p(3)) that cause the three lines they correspond to to intersect at one point and also minimize the equation:
summation(j:1-3, (o(j) - p(j))^2)
What I am asked to do is reformulate the problem as a constrained optimization problem and to describe the constraints in mathematical expressions. I do not get exactly what this is asking me to do and am a little lost.