This is an announcement for the paper "Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces" by Antonio Falco and Anthony Nouy. Abstract: 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 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 Proper Generalized Decompositions for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space. Archive classification: math.NA math.FA math.OC Mathematics Subject Classification: 65K10, 49M29 Submitted from: afalco@uch.ceu.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1106.4424 or http://arXiv.org/abs/1106.4424