Barzilai-Borwein Step

Problem

Compute both Barzilai-Borwein step sizes from s = x_new - x_old and y = grad_new - grad_old.

BB1 is (s dot s) / (s dot y) and BB2 is (s dot y) / (y dot y). Return [bb1, bb2], using 0.0 for either value whose denominator is zero.

Hint

BB1 and BB2 differ by which side of the secant equation they minimize.

case 1

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

expected: [0.6666666666666666,0.6]

case 2

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

expected: [0.5,0.5]

case 3

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

expected: [0,0]

case 4

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

expected: [2,1]

Starter codePython

def barzilai_borwein_step(s, y):
    # Returns [bb1, bb2]
    # Your code here
    pass

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