Trust-Region Newton 1D

Problem

Take a trust-region-clipped Newton step in 1D.

When hess > 0 the step is -grad / hess clipped to [-radius, radius]. When hess <= 0 move against the gradient by radius, or use delta = 0 when grad is 0. Return [x + delta, delta].

Hint

Negative curvature means the quadratic is unbounded below; walk to the trust boundary.

Test cases

case 1

in: [1,2,4,10]

expected: [0.5,-0.5]

case 2

in: [1,8,2,2]

expected: [-1,-2]

case 3

in: [0,-3,-1,1]

expected: [1,1]

case 4

in: [1,0,0,1]

expected: [1,0]

Starter codePython

def trust_region_newton_1d(x, grad, hess, radius):
    # Returns [x_new, delta]
    # Your code here
    pass

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