Neural Geometry for Constrained Optimization
Giansalvo Cirrincione, Maurizio Cirrincione, Sabine Van Huffel · 1999
Many engineering problems require the on-line solution of constrained optimization problems. This paper proposes, as an original contribution, particular neural architectures, called neural solids, whose interconnections represent the required constraints. The first neural solid presented here is the neural triangle whose learning law solves simple orthogonality problems. This solid is the basis for more complex architectures solving problems with orthogonality constraints: the paper presents and yields examples of the neural decomposer which can be used for computer vision applications and the EXIN NSVD neural network which yields the singular value decomposition of a given matrix. These neural networks are not only important because they give a fast solution of the optimization, but, above all, because they introduce a new technique which can be extended to more complex constrained optimization problems. Keywords--- Backpropagation, Features, Hopfield networks, Image Matching, Neura...