Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming

Algorithm 2

%Sgen: Generate random solvable recourse problems:

%Input: m,n,d(ensity); Output: W,q,𝜉;

m=input(’Enter 𝑛₂:’)

n=input(’Enter 𝑚₂:’)

d=input(’Enter d:’)

pl=inline(’(abs(x)+x)/2’)

W=sprand(𝑛₂,𝑚₂,d);W=100*(W-0.5*spones(W));

z=sparse(10*pl(rand(𝑚₂,1)));

q=W*z;

y=spdiags((sign(pl(rand(𝑛₂,1)-rand(𝑛₂,1)))),0,𝑛₂,𝑛₂)

*5*((rand(𝑛₂,1)-rand(𝑛₂,1)));

ξ=W’*y-10*spdiags((ones(𝑚₂,1)-sign(z)),0,𝑚₂,𝑚₂)*ones(𝑚₂,1));

format short e; nnz(W)/prod(size(W))