66 research outputs found
Identification of Structured LTI MIMO State-Space Models
The identification of structured state-space model has been intensively
studied for a long time but still has not been adequately addressed. The main
challenge is that the involved estimation problem is a non-convex (or bilinear)
optimization problem. This paper is devoted to developing an identification
method which aims to find the global optimal solution under mild computational
burden. Key to the developed identification algorithm is to transform a
bilinear estimation to a rank constrained optimization problem and further a
difference of convex programming (DCP) problem. The initial condition for the
DCP problem is obtained by solving its convex part of the optimization problem
which happens to be a nuclear norm regularized optimization problem. Since the
nuclear norm regularized optimization is the closest convex form of the
low-rank constrained estimation problem, the obtained initial condition is
always of high quality which provides the DCP problem a good starting point.
The DCP problem is then solved by the sequential convex programming method.
Finally, numerical examples are included to show the effectiveness of the
developed identification algorithm.Comment: Accepted to IEEE Conference on Decision and Control (CDC) 201
Generalized Nonconvex Nonsmooth Low-Rank Minimization
As surrogate functions of -norm, many nonconvex penalty functions have
been proposed to enhance the sparse vector recovery. It is easy to extend these
nonconvex penalty functions on singular values of a matrix to enhance low-rank
matrix recovery. However, different from convex optimization, solving the
nonconvex low-rank minimization problem is much more challenging than the
nonconvex sparse minimization problem. We observe that all the existing
nonconvex penalty functions are concave and monotonically increasing on
. Thus their gradients are decreasing functions. Based on this
property, we propose an Iteratively Reweighted Nuclear Norm (IRNN) algorithm to
solve the nonconvex nonsmooth low-rank minimization problem. IRNN iteratively
solves a Weighted Singular Value Thresholding (WSVT) problem. By setting the
weight vector as the gradient of the concave penalty function, the WSVT problem
has a closed form solution. In theory, we prove that IRNN decreases the
objective function value monotonically, and any limit point is a stationary
point. Extensive experiments on both synthetic data and real images demonstrate
that IRNN enhances the low-rank matrix recovery compared with state-of-the-art
convex algorithms.Comment: IEEE International Conference on Computer Vision and Pattern
Recognition, 201
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