Robust Counterpart Check

Problem

Check whether x satisfies the robust counterpart of a box-uncertain constraint.

With coefficients a_i uncertain in [a_i - d_i, a_i + d_i], the worst case uses a_i + d_i for positive x_i and a_i - d_i for negative x_i. Return True when the worst-case left-hand side is at most b + tol.

Hint

The sign of x decides which uncertainty endpoint is worst.

Test cases

case 1

in: [[1,1],[0.1,0.1],[1,1],2.1,1e-9]

expected: false

case 2

in: [[1,1],[0.1,0.1],[1,1],2,1e-9]

expected: false

case 3

in: [[1,-2],[0.5,0.5],[2,3],-1,1e-9]

expected: true

Starter codePython

def robust_counterpart_check(a, d, x, b, tol):
    # Your code here
    pass

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