human
Can you provide a Python program to determine the optimal launch azimuth and elevation angles, in order to maximize the likelihood of landing in a particular region given the following:
I am working on the file "Simulation_and_Optimization/Launcher_Settings_Optimization.ipynb".
The first task is:
The purpose of this notebook is to determine the optimal launch azimuth and elevation angles, in order to maximize the likelihood of landing in a particular region. Eventually, this should be expanded to enable input of day-of wind measurements so that we can determine these settings on the day of the launch. We may need to optimize the trajectory simulation code for this purpose, perhaps with less degrees of freedom, since it is currently fairly slow.
This program has essentially the same structure as the MDO and differs only in how trajectory performance is evaluated and which parameters are held constant or optimized over. Examination of the differences should enable one to make similar programs for different but related purposes.
Functions of Merit
We chose to abstract all of the functions used within the merit function for increased flexibility, ease of reading, and later utility. We use convex functions four our optimization, but we don't use much of the theory of convex optimization.

objective_additive is arbitrarily constructed. It is
appropriate for vector-valued measurements,
not normalized,
squared to reward (or punish) relative to the distance from nominal value, and
divided by two for aesthetic reasons.

objective is arbitrarily constructed. It is
normalized (by a somewhat arbitrary constant) to bring it into the same range as constraints,
squared to reward (or punish) relative to the distance from nominal value, and
divided by two so that our nominal value is 0.5 instead of 1.0.

exact is less arbitrarily constructed. It is
squared to be horizontally symmetric (which could also be obtained by absolute value),
determined by the distance from a constant, and
divided by two is for aesthetic value.

exterior is not particularly arbitrary. It is
boolean so that we can specify whether it is minimizing or maximizing its variable,
0 when the inequality is satisfied, otherwise it is just as punishing as exact.

barrier comes in two flavors, one of which is not used here. It is
boolean so that we can...
Can you write Python program for it?
assistant
#Here is Python program to determine the optimal launch azimuth and elevation angles, in order to maximize the likelihood of landing in a particular region.

# all of our comparisons are ratios instead of subtractions because
# it's normalized, instead of dependent on magnitudes of variables and constraints

def objective_additive(var, cons):
    return np.linalg.norm(var - cons)**2 / 2

# minimize this, **2 makes it well behaved w.r.t. when var=cons
def objective(var, cons):
    return (var/cons)**2 / 2

# **2 because i like it more than abs(), but that also works
def exact(var, cons):
    return (var/cons - 1)**2 / 2

# this is your basic exterior penalty, either punishes for unfeasibility or is inactive
def exterior(var, cons, good_if_less_than=False):
    if good_if_less_than:
        return max(0, var/cons - 1)**2 / 2
    else:
        return max(0, -(var/cons - 1))**2 / 2

# this barrier function restricts our objective function to the strictly feasible region
# make rockets great again, build that wall, etc, watch out for undefined operations
def barrier(var, cons, int_point=False, good_if_less_than=True):
    global dbz
    try: # just in case we accidentally leave feasible region
        if not int_point:
            if good_if_less_than:
                return -log(-(var/cons - 1))
            else:
                return -log(var/cons - 1)
        elif int_point:
            def interior(g): return 1/g # in case we don't like logarithms, which is a mistake
            if good_if_less_than:
                return -interior(var/cons - 1)
            else:
                return -interior(-(var/cons - 1))
    except:
        return float('inf') # ordinarily, this is bad practice since it could confuse the optimizer
                            # however, since this is a barrier function not an ordinary penalty, i think it's fine