Proximal Operator of Quadratic

Problem

The proximal operator of t * 0.5 * a * (x - c)^2 is (v + t a c) / (1 + t a).

Given v, c, the step t, and the curvature a > 0, return the prox value.

Hint

Solve the scalar problem min_x 0.5 (x - v)^2 + t * 0.5 * a (x - c)^2.

case 1

in: [1,0,0.5,2]

expected: 0.5

case 2

in: [3,1,1,1]

expected: 2

case 3

in: [0,5,2,0.5]

expected: 2.5

Starter codePython

def proximal_operator_quadratic(v, c, t, a):
    # Your code here
    pass

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