Improving on Gradient Descent Algorithm I have tried to solve the problem 607 in Project Euler  using the Gradient Descent Algorithm. While I’m getting the answer right I’m not sure if I have used the gradient algorithm correctly or coded it efficiently in Python. I’ll appreciate any guidance or suggestions to improve.

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Jan 11 18:48:41 2018

"""

# Gradient Descent Algorithm

import numpy as np
import time
import random

def duration(points): # Duration as the objective function
    speed = [ 10, 9, 8, 7, 6, 5,10 ]
    duration=0
    for i in range(0,len(speed)):
        distance = ((points[i+1,0]-points[i,0])**2 + (points[i+1,1]-points[i,1])**2)**0.5
        duration += distance / speed[i]
    return duration

def gradient_function(points): # Gradient: Partial differential of duration function f(x) wrt x
    speed = [ 10, 9, 8, 7, 6, 5,10 ]
    gradient = 0 #np.zeros((8,2))
    for i in range(0,len(speed)):
        gradient += ((points[i+1,0]-points[i,0])/(speed[i]*((points[i+1,0]-points[i,0])**2 + (points[i+1,1]-points[i,1])**2)**0.5))
    return gradient

# Generate randon number between -1 and +1
def myrand():
    seed = random.random() * 2 - 1
    return seed

# Compute x = x0-delta*gradient
def gradient_descent(points,delta):
    old_Duration = duration(points)
    new_Duration = old_Duration - delta * gradient_function(points)
    if myrand() &gt; 0:
        delta = -delta
    id = int(random.random()*6)+1
    points[id,0] += delta 
    new_Duration = old_Duration - (1+ delta)*delta * gradient_function(points)
    if (duration(points) &gt;= old_Duration):
        points[id,0] -= delta
        new_Duration = old_Duration - (1-delta)*delta * gradient_function(points)
    return new_Duration

# Floating Point Range Function
def frange(start, stop, step):
    i = start
    while i &gt;= stop:
        yield i
        i /= step
    return step

# Calculate the Minimum Days    
def min_days():
    normal_terrain = ((100 / np.sqrt(2) - 50) / 2)
    marsh = 10.
    ini_xy = [ 0., normal_terrain, marsh, marsh, marsh, marsh, marsh, normal_terrain ]
    y_coords = []
    x_coords = []
    k = 0
    for i in range(0,len(ini_xy)):
        k += ini_xy[i]
        y_coords.append(k)
        x_coords.append(k)
    points = (np.stack((x_coords,y_coords), axis=-1))

    for delta in frange(1e-2, 1e-10, 10):
        for i in range(10000):
            gradient_descent(points,delta)
    min_days = gradient_descent(points,delta)
    return min_days

start = time.time()
answer = min_days()
elapsed = time.time() - start
print("\nThe Minimum Days is %s found in %s seconds" % (answer,elapsed))
For Python 3.x you do not need to specify the encoding type you chose because it chips by default with UTF-8. So you can safely remove the directive: # -*- coding: utf-8 -*-
You should use timeit over time because the first one is more accurate.
As per PEP 8, you should leave 2 blank lines between the last import statement and the start of your code.
Better if you run this module by putting the guard if __name__ == "__main__"
The inline comments you used would be better used as docstrings instead.