A numerical method is proposed to compute a low-rank Galerkin approximationto the solution of a parametric or stochastic equation in a non-intrusivefashion. The considered nonlinear problems are associated with the minimizationof a parameterized differentiable convex functional. We first introduce abilinear parameterization of fixed-rank tensors and employ an alternatingminimization scheme for computing the low-rank approximation. In keeping withthe idea of non-intrusiveness, at each step of the algorithm the minimizationsare carried out with a quasi-Newton method to avoid the computation of theHessian. The algorithm is made non-intrusive through the use of numericalintegration. It only requires the evaluation of residuals at specific parametervalues. The algorithm is then applied to two numerical examples.
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