Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces

Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called proper generalized decompositions (PGD) methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated PGDs for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.