[Solved] You want to minimize f(x) = (x[0]-1)^2 + (x[1]-2)^2 subject to nonlinear constraints x[0]^2 +... Which is the correct way to define these constraints for scipy.optimize.minimize with method 'SLSQP'? | SciPy

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You want to minimize f(x) = (x[0]-1)^2 + (x[1]-2)^2 subject to nonlinear constraints x[0]^2 + x[1]^2 <= 2 and x[0] - x[1] >= 0. Which is the correct way to define these constraints for scipy.optimize.minimize with method 'SLSQP'?

A[{'type': 'ineq', 'fun': lambda x: 2 - (x[0]**2 + x[1]**2)}, {'type': 'ineq', 'fun': lambda x: x[0] - x[1]}]

B[{'type': 'eq', 'fun': lambda x: 2 - (x[0]**2 + x[1]**2)}, {'type': 'eq', 'fun': lambda x: x[0] - x[1]}]

C[{'type': 'ineq', 'fun': lambda x: (x[0]**2 + x[1]**2) - 2}, {'type': 'ineq', 'fun': lambda x: x[1] - x[0]}]

D[{'type': 'ineq', 'fun': lambda x: (x[0]**2 + x[1]**2) - 2}, {'type': 'ineq', 'fun': lambda x: x[0] - x[1]}]

Step-by-Step Solution

Solution:

Step 1: Translate constraints to 'ineq' form
For 'ineq', function must be >= 0. So x0^2+x1^2 <= 2 becomes 2 - (x0^2+x1^2) >= 0.
Step 2: Check second constraint
x0 - x1 >= 0 is already in correct form.
Final Answer:
[{'type': 'ineq', 'fun': lambda x: 2 - (x[0]**2 + x[1]**2)}, {'type': 'ineq', 'fun': lambda x: x[0] - x[1]}] -> Option A
Quick Check:
Constraints must be 'ineq' with function >= 0 [OK]

Quick Trick: Rewrite constraints so function >= 0 for 'ineq' type [OK]

Common Mistakes:

Using 'eq' instead of 'ineq' for inequalities
Reversing inequality signs
Not rewriting constraints to >= 0 form

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Which is the correct way to define these constraints for scipy.optimize.minimize with method 'SLSQP'?

Step 1: Translate constraints to 'ineq' form

Step 2: Check second constraint

Final Answer:

Quick Check:

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