I'm sorry but if X'X=I, unless I'm mistaken, X'=inv(X). so Inv(x'x) =I so inv(x'x)x'y =x'y=olsbeta^=inv(x)y. Using subgradient methods with this (see Wikipedia) gives beta^j=SNlambda(beta^olsj)=beta^olsj*max(0,1-Nlambda/(abs(beta^olsj)). See the link below for details with clearer notation. Best wishes.