  A numerical method is proposed to compute a low-rank Galerkin approximation
to the solution of a parametric or stochastic equation in a non-intrusive
fashion. The considered nonlinear problems are associated with the minimization
of a parameterized differentiable convex functional. We first introduce a
bilinear parameterization of fixed-rank tensors and employ an alternating
minimization scheme for computing the low-rank approximation. In keeping with
the idea of non-intrusiveness, at each step of the algorithm the minimizations
are carried out with a quasi-Newton method to avoid the computation of the
Hessian. The algorithm is made non-intrusive through the use of numerical
integration. It only requires the evaluation of residuals at specific parameter
values. The algorithm is then applied to two numerical examples.
