655 research outputs found
A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality
Symmetric nonnegative matrix factorization (SymNMF) has important
applications in data analytics problems such as document clustering, community
detection and image segmentation. In this paper, we propose a novel nonconvex
variable splitting method for solving SymNMF. The proposed algorithm is
guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the
nonconvex SymNMF problem. Furthermore, it achieves a global sublinear
convergence rate. We also show that the algorithm can be efficiently
implemented in parallel. Further, sufficient conditions are provided which
guarantee the global and local optimality of the obtained solutions. Extensive
numerical results performed on both synthetic and real data sets suggest that
the proposed algorithm converges quickly to a local minimum solution.Comment: IEEE Transactions on Signal Processing (to appear
Multi-Agent Distributed Optimization via Inexact Consensus ADMM
Multi-agent distributed consensus optimization problems arise in many signal
processing applications. Recently, the alternating direction method of
multipliers (ADMM) has been used for solving this family of problems. ADMM
based distributed optimization method is shown to have faster convergence rate
compared with classic methods based on consensus subgradient, but can be
computationally expensive, especially for problems with complicated structures
or large dimensions. In this paper, we propose low-complexity algorithms that
can reduce the overall computational cost of consensus ADMM by an order of
magnitude for certain large-scale problems. Central to the proposed algorithms
is the use of an inexact step for each ADMM update, which enables the agents to
perform cheap computation at each iteration. Our convergence analyses show that
the proposed methods converge well under some convexity assumptions. Numerical
results show that the proposed algorithms offer considerably lower
computational complexity than the standard ADMM based distributed optimization
methods.Comment: submitted to IEEE Trans. Signal Processing; Revised April 2014 and
August 201
Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers
In this paper, we consider solving multiple-block separable convex
minimization problems using alternating direction method of multipliers (ADMM).
Motivated by the fact that the existing convergence theory for ADMM is mostly
limited to the two-block case, we analyze in this paper, both theoretically and
numerically, a new strategy that first transforms a multi-block problem into an
equivalent two-block problem (either in the primal domain or in the dual
domain) and then solves it using the standard two-block ADMM. In particular, we
derive convergence results for this two-block ADMM approach to solve
multi-block separable convex minimization problems, including an improved
O(1/\epsilon) iteration complexity result. Moreover, we compare the numerical
efficiency of this approach with the standard multi-block ADMM on several
separable convex minimization problems which include basis pursuit, robust
principal component analysis and latent variable Gaussian graphical model
selection. The numerical results show that the multiple-block ADMM, although
lacks theoretical convergence guarantees, typically outperforms two-block
ADMMs
Outage Constrained Robust Secure Transmission for MISO Wiretap Channels
In this paper we consider the robust secure beamformer design for MISO
wiretap channels. Assume that the eavesdroppers' channels are only partially
available at the transmitter, we seek to maximize the secrecy rate under the
transmit power and secrecy rate outage probability constraint. The outage
probability constraint requires that the secrecy rate exceeds certain threshold
with high probability. Therefore including such constraint in the design
naturally ensures the desired robustness. Unfortunately, the presence of the
probabilistic constraints makes the problem non-convex and hence difficult to
solve. In this paper, we investigate the outage probability constrained secrecy
rate maximization problem using a novel two-step approach. Under a wide range
of uncertainty models, our developed algorithms can obtain high-quality
solutions, sometimes even exact global solutions, for the robust secure
beamformer design problem. Simulation results are presented to verify the
effectiveness and robustness of the proposed algorithms
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