Documenting optimization Approach from old repository

optimization/Optimization Project Details.md

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+# Optimization
+
+## Goal
+
+The goal of this project is to find the optimal velocity of the vehicle at any given time based on the predicted net energy consumption of the vehicle. 
+
+## Approach
+
+Optimization algorithms utilize a Loss function (known as the objective) that needs to be minimized in order to find the value of the velocity at the global minimum of this loss function. 
+
+From research done in this ticket: https://uwmidsun.atlassian.net/browse/STRAT15-28?atlOrigin=eyJpIjoiMjA1Y2QzZjhlMzI3NDI2MThjZTBiYzhmOTNlMWQwMjMiLCJwIjoiaiJ9 we have decided to go forward with **[`scipy.optimize.minimize()`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)** with the `trust-constr` option for the minimize function. 
+
+The objective function takes a `v_profile` and returns the energy used by the car. This is the loss function that the `optimize` function needs to minimize in order to find the optimal velocity which is the `x` variable of the solution. 
+
+We start with the elevations and we calculate angle of elevations using the formula 
+
+$$
+\theta = \arctan(\dfrac{\text{elevation}}{\text{distance}})
+$$
+
+We create a list of these ‘pitches’ which is known as the `e_profile` .
+
+Then we generate the initial profile using the following parameters:
+
+```python
+"""
+    :param time: Maximum allowable time to cover a distance in seconds
+    :param distance: Distance to be covered in meters
+    :param e_profile: List of pitches the car must travel
+    :param min_velocity: Minimum allowable velocity
+    :param stop_profile: List of indices where car must stop
+"""
+```