Bounds and constraints in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define bounds for the variables in the optimization problem.

SciPy

from scipy.optimize import minimize

bounds = [[1]]

result = minimize(lambda x: x[0]**2 + x[1]**2, [1, 1], bounds=bounds)
print(result.x)

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A(0, None), (0, None)

B[0, None], [0, None]

C[(0, None), (0, None)]

D0, None, 0, None

Attempts:

3 left

💡 Hint

Common Mistakes

Using a tuple instead of a list for bounds

Not enclosing bounds in a list

Using separate tuples without a list

Bounds in scipy.optimize.minimize must be a list of tuples, each tuple specifying (min, max) for a variable.

2fill in blank

medium

Complete the code to define a linear constraint for the optimization problem.

SciPy

from scipy.optimize import LinearConstraint

constraint = LinearConstraint([1], 0, 10)

print(constraint)

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A[1, 2]

B[1, 2, 3]

C[[1], [2]]

D[[1, 2]]

Attempts:

3 left

💡 Hint

Common Mistakes

Using a 1D list instead of 2D list

Using incorrect dimensions for the constraint matrix

LinearConstraint expects a 2D array or list of lists for the constraint matrix.

3fill in blank

hard

Fix the error in the code by completing the constraint definition correctly.

SciPy

from scipy.optimize import minimize, LinearConstraint
import numpy as np

A = np.array([[1, 2], [3, 4]])
constraint = LinearConstraint(A, [1], [10, 20])

result = minimize(lambda x: x[0]**2 + x[1]**2, [1, 1], constraints=[constraint])
print(result.x)

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A[0, 0]

B[5, 15]

C[10, 20]

D[1, 2]

Attempts:

3 left

💡 Hint

Common Mistakes

Setting lower bounds higher than upper bounds

Using incorrect array sizes for bounds

The lower bounds must be less than or equal to the upper bounds. Using zeros as lower bounds fits the problem constraints.

4fill in blank

hard

Fill both blanks to create a nonlinear constraint function and define it properly.

SciPy

from scipy.optimize import minimize, NonlinearConstraint
import numpy as np

def constraint_func(x):
    return x[0]**2 + x[1]**2 - [1]

nlc = NonlinearConstraint(constraint_func, 0, [2])

result = minimize(lambda x: x[0] + x[1], [1, 1], constraints=[nlc])
print(result.x)

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A1

B2

C3

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using bounds that do not match the function output range

Confusing the constant subtracted in the function

The constraint function subtracts 1, so the lower bound is 0 and upper bound is 2 to allow values between 1 and 3 for the sum of squares.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that filters variables based on bounds.

SciPy

variables = {'x': 5, 'y': 10, 'z': 15}
bounds = {'x': (0, 10), 'y': (5, 15), 'z': (10, 20)}
filtered = [1]: variables[[2]] for [3] in variables if bounds[[3]][0] <= variables[[3]] <= bounds[[3]][1]}
print(filtered)

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Ak

Bv

Dkey

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently

Using values instead of keys in the comprehension

The comprehension uses 'k' as the variable name for keys to filter variables within their bounds.