Complementary Slackness Check

Problem

Complementary slackness for a KKT point requires lambda_i * g_i(x) = 0 for every inequality constraint, together with nonnegative multipliers.

Given the constraint values gaps = g_i(x) and the multipliers, return True when every multiplier is nonnegative and every product is within tol (default 1e-9) of zero.

Hint

An inactive constraint must carry a zero multiplier, and an active one may carry a positive multiplier.

Test cases

case 1

in: [[0,1.5],[2,0]]

expected: true

case 2

in: [[1,1],[1,1]]

expected: false

case 3

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

expected: true

case 4

in: [[1,0],[-1,0]]

expected: false

Starter codePython

def complementary_slackness(gaps, multipliers, tol=1e-9):
    # Your code here
    pass

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