Quasi-Newton methods on Grassmannians and multilinear approximations of tensors. (English) Zbl 1226.65058
The authors propose quasi-Newton and limited memory quasi-Newton algorithms for functions defined on a Grassmannian Gr\((n, r)\) as well as a product of Grassmannians Gr\((n_1, r_1) \times \dots \times\) Gr\((n_k, r_k)\), with Broyden-Fletcher-Shanno-Goldfarb (BFGS) and limited memory BFGS updates. By focusing on the local coordinates approach they show that their BFGS update shares the same well-known optimality property of its Euclidean counterpart.
Reviewer: Constantin Popa (Constanţa)
MSC:
65K05 | Numerical mathematical programming methods |
90C53 | Methods of quasi-Newton type |
15A69 | Multilinear algebra, tensor calculus |
14M15 | Grassmannians, Schubert varieties, flag manifolds |
90C30 | Nonlinear programming |
53A45 | Differential geometric aspects in vector and tensor analysis |