Optimization Quiz

Quiz 1

 

 

Quiz 2

from elice_utils import EliceUtils

from scipy.optimize import linprog

import numpy as np

elice_utils = EliceUtils()

def main():

    # Consider what each variable represents in the linprog function

    c = [-0.5, -1] #TODO

 

    A = [[1, 1], [1, 8/3]] #TODO

    b = [2, 4] #TODO

   

    x0_bounds = [0, 1.5] #TODO

    x1_bounds = [0, None] #TODO

   

    # DO NOT TOUCH THIS LINE BELOW

    res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds], method='interior-point')

    print(f'Optimal values are x1 = {round(res.x[0], 1)} and x2 = {round(res.x[1], 1)}')

    ''' round는 반올림 함수이다

    round(수, 반올림해 표시할 자리수); round(3.7, 1)이면 3.7을 소수점 첫번째 자리까지 나타낸다는 뜻'''

    return res.x[0], res.x[1]

if __name__ == "__main__":

    main()

 

 

Quiz 3

from elice_utils import EliceUtils

import numpy as np

import matplotlib.pyplot as plt

from scipy.optimize import minimize

elice_utils = EliceUtils()

#Do not touch this function

def plt_show():

    plt.savefig("fig")

    elice_utils.send_image("fig.png")

def main():

    # Consider what each variable represents in the linprog function

    # Constants

    v0 = 10 #TODO

    g = 9.8  # g=9.8m/s^2

    # Time array and height calculation

    t = np.arange(0, 2.1, 0.1)

    #Cost Function

    h = v0 * t - 0.5 * g * t ** 2 #TODO

    # Plot

    plt.plot(t, h)

    plt.grid(True)

    plt.xlabel('t')

    plt.ylabel('h')

    plt_show()

    # Objective function

    def objective(t):

        return -v0 * t + 0.5 * g * t ** 2 #TODO

    # Bounds

    bounds = [(0, 5)]

    # Solve

    res = minimize(objective, x0=2, bounds=bounds)  # starting from x0=2 for better convergence

    '''minimize 함수에 대한 설명은 다음 링크에

    https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html'''

    #How can you obtain x from res?

    x = res.x[0] #TODO

    hmax = v0 * x - 0.5 * g * x ** 2 #TODO

 

    print(f'Optimal value t = {x:.2f} and the max height h = {hmax:.2f}')

    return x, hmax

if __name__ == "__main__":

    main()