In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of stat...

It is known that quasi–Newton updates can be characterized by variational means, sometimes in more than one way. This paper has two main goals. We first formulate variational problems appearing in quasi-Newton methods within the vector space of symmetric matrices. This simplifies both their formulations and their subsequent solutions. We then construct, for the first time, duals of the variatio...

We introduce a general criterion for blindly extracting a subset of sources in instantaneous mixtures. We derive the corresponding estimation equations and generalize them based on arbitrary nonlinear separating functions. A quasi-Newton algorithm for minimizing the criterion is presented, which reduces to the FastICA algorithm in the case when only one source is extracted. The asymptotic distr...

The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak–Ribière–Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the object...

V sequence fxkg. Similar result is also true for quasiNewton methods with trust region (see [16]). Another type of special quasi-Newton methods is that the quasi-Newton matrices are sparse. It is quite often that large-scale problems have separable structure, which leads to special structure of the Hessian matrices. In such cases we can require the quasiNewton matrices to have similar structures.

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We study Newton’s method and method based on linearization for solving quasi-variational inequalities in a finite-dimensional real vector space. Projection methods were the most studied methods for solving quasi-variational inequalities and they have linear rates of the convergence. In the paper we establish sufficient conditions for the convergence of Newton’s method and method of linearizatio...

In this report we present computational methods for the best multilinear rank approximation problem. We consider algorithms build on quasi-Newton methods operating on product of Grassmann manifolds. Specifically we test and compare methods based on BFGS and L-BFGS updates in local and global coordinates with the Newton-Grassmann and alternating least squares methods. The performance of the quas...