1: set k = 0

2: set ℓ−1 = 0

3: set $x^k=\overline{x}$

4: while k < K do

5: set n = 0

6:   set ℓk = rand(k, ℓk−1)

7:   set xk,n = xk

8:   while n < N do

9:     set vk,n = ϕ′(xk,n)

10:     set βk,n = αℓk

11:     set loop = true

12:     while loop do

13:       set zk,n = xk,n + βk,nvk,n

14:       if ϕ(zk,n) ≤ ϕ(xk,n) then

15:         set xk,n = zk,n

16:         set loop = false

17:       end if

18:       set ℓk = ℓk + 1

19:     end while

20:     set n = n + 1

21:   end while

22:   set xk+1 = PT(xk,N)

23:   set k = k + 1

24: end while