A new approach for convolutive blind source separation (BSS) using penalty functions is proposed in this paper. Motivated by nonlinear programming techniques for the constrained optimization problem, it converts the convolutive BSS into a joint diagonalization problem with unconstrained optimization. Theoretical analyses together with numerical evaluations reveal that the proposed method not on...

We introduce a trust region algorithm for minimization of nons-mooth functions with linear constraints. At each iteration, the objective function is approximated by a model fuction that satisses a set of assumptions stated recently by Qi and Sun in the context of unconstrained nonsmooth optimization. The trust region iteration begins with the resolution of an \easy problem", as in recent works ...

The estimation of variance-covariance matrices in situations that involve the optimization of an objective function (e.g. a log-likelihood function) is usually a difficult numerical problem, since the resulting estimates should be positive semi-definite matrices. We can either use constrained optimization, or employ a parameterization that enforces this condition. We describe here five differen...

In this paper we carry out a theoretical analysis of two regularization methods for nonlinear ill-posed problems. The rst is a penalty method called Tikhonov regularization, in which one solves an unconstrained optimization problem while the second is based on a constrained optimization problem. For each method we examine the well-posedness of the respective optimization problem. We then show s...