KKT Condition Check

Problem

Check the KKT conditions for minimizing f(x, y) = 0.5*a*x^2 + 0.5*b*y^2 subject to g(x, y) = d - x - y <= 0.

The Lagrangian is f + lambda*g. Return True when all hold within the tolerance: a*x - lambda == 0, b*y - lambda == 0, g <= 0, lambda >= 0, and lambda*g == 0.

Hint

Stationarity, primal feasibility, dual feasibility, and complementary slackness must all hold.

Test cases

case 1

in: [2,2,1,0.5,0.5,1]

expected: true

case 2

in: [2,2,1,0.5,0.5,0]

expected: false

case 3

in: [2,2,1,0.3,0.5,1]

expected: false

case 4

in: [1,3,2,1.5,0.5,1.5]

expected: true

case 5

in: [2,2,0,0,0,0]

expected: true

Starter codePython

def kkt_check(a, b, d, x, y, lam, tol=1e-9):
    # Your code here
    pass

5 test cases · run your code against them in the editor