joint work with Paul Goulart, Yuji Nakatsukasa
We present an active-set algorithm for the minimisation of a non-convex quadratic function subject to linear constraints and a single norm constraint. The suggested algorithm works by solving a series of Trust Region Subproblems (TRS) the global solution of which has been studied extensively in the literature. We extend these results by showing that non-global minima of the TRS, or a certificate of their absence, can be also calculated efficiently by solving a single eigenproblem. We demonstrate the usefulness of the algorithm in solving Sparse PCA and extended Trust Region Subproblems
joint work with Felix Krahmer, Max Pfeffer
The problem of recovering a row or column sparse low-rank matrix from linear measurements arises for instance in sparse blind deconvolution. We consider non-convex optimization algorithms for such problems that combine the idea of an ADMM method for sparse recovery with Riemannian optimization on the low-rank manifold and thresholding.
joint work with Akiko Takeda, Ivan Markovsky, Ting Kei Pong
In this talk, we consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and several nonsmooth functions, some of which are composed with linear maps. This includes the problems arising from system identification with multiple rank-constraints, each of which involves Hankel structure. To solve it, we propose a successive DC approximation method, which makes use of the DC structure of the Moreau envelope. We prove the convergence of the method under suitable assumptions and discuss how it can be applied to concrete applications.