53 research outputs found
Energy efficiency optimization in MIMO interference channels: A successive pseudoconvex approximation approach
In this paper, we consider the (global and sum) energy efficiency
optimization problem in downlink multi-input multi-output multi-cell systems,
where all users suffer from multi-user interference. This is a challenging
problem due to several reasons: 1) it is a nonconvex fractional programming
problem, 2) the transmission rate functions are characterized by
(complex-valued) transmit covariance matrices, and 3) the processing-related
power consumption may depend on the transmission rate. We tackle this problem
by the successive pseudoconvex approximation approach, and we argue that
pseudoconvex optimization plays a fundamental role in designing novel iterative
algorithms, not only because every locally optimal point of a pseudoconvex
optimization problem is also globally optimal, but also because a descent
direction is easily obtained from every optimal point of a pseudoconvex
optimization problem. The proposed algorithms have the following advantages: 1)
fast convergence as the structure of the original optimization problem is
preserved as much as possible in the approximate problem solved in each
iteration, 2) easy implementation as each approximate problem is suitable for
parallel computation and its solution has a closed-form expression, and 3)
guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The
advantages of the proposed algorithm are also illustrated numerically.Comment: submitted to IEEE Transactions on Signal Processin
Successive Convex Approximation Algorithms for Sparse Signal Estimation with Nonconvex Regularizations
In this paper, we propose a successive convex approximation framework for
sparse optimization where the nonsmooth regularization function in the
objective function is nonconvex and it can be written as the difference of two
convex functions. The proposed framework is based on a nontrivial combination
of the majorization-minimization framework and the successive convex
approximation framework proposed in literature for a convex regularization
function. The proposed framework has several attractive features, namely, i)
flexibility, as different choices of the approximate function lead to different
type of algorithms; ii) fast convergence, as the problem structure can be
better exploited by a proper choice of the approximate function and the
stepsize is calculated by the line search; iii) low complexity, as the
approximate function is convex and the line search scheme is carried out over a
differentiable function; iv) guaranteed convergence to a stationary point. We
demonstrate these features by two example applications in subspace learning,
namely, the network anomaly detection problem and the sparse subspace
clustering problem. Customizing the proposed framework by adopting the
best-response type approximation, we obtain soft-thresholding with exact line
search algorithms for which all elements of the unknown parameter are updated
in parallel according to closed-form expressions. The attractive features of
the proposed algorithms are illustrated numerically.Comment: submitted to IEEE Journal of Selected Topics in Signal Processing,
special issue in Robust Subspace Learnin
A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank Minimization
In this paper, we propose a convergent parallel best-response algorithm with
the exact line search for the nondifferentiable nonconvex sparsity-regularized
rank minimization problem. On the one hand, it exhibits a faster convergence
than subgradient algorithms and block coordinate descent algorithms. On the
other hand, its convergence to a stationary point is guaranteed, while ADMM
algorithms only converge for convex problems. Furthermore, the exact line
search procedure in the proposed algorithm is performed efficiently in
closed-form to avoid the meticulous choice of stepsizes, which is however a
common bottleneck in subgradient algorithms and successive convex approximation
algorithms. Finally, the proposed algorithm is numerically tested.Comment: Submitted to IEEE ICASSP 201
Edge and Central Cloud Computing: A Perfect Pairing for High Energy Efficiency and Low-latency
In this paper, we study the coexistence and synergy between edge and central
cloud computing in a heterogeneous cellular network (HetNet), which contains a
multi-antenna macro base station (MBS), multiple multi-antenna small base
stations (SBSs) and multiple single-antenna user equipment (UEs). The SBSs are
empowered by edge clouds offering limited computing services for UEs, whereas
the MBS provides high-performance central cloud computing services to UEs via a
restricted multiple-input multiple-output (MIMO) backhaul to their associated
SBSs. With processing latency constraints at the central and edge networks, we
aim to minimize the system energy consumption used for task offloading and
computation. The problem is formulated by jointly optimizing the cloud
selection, the UEs' transmit powers, the SBSs' receive beamformers, and the
SBSs' transmit covariance matrices, which is {a mixed-integer and non-convex
optimization problem}. Based on methods such as decomposition approach and
successive pseudoconvex approach, a tractable solution is proposed via an
iterative algorithm. The simulation results show that our proposed solution can
achieve great performance gain over conventional schemes using edge or central
cloud alone. Also, with large-scale antennas at the MBS, the massive MIMO
backhaul can significantly reduce the complexity of the proposed algorithm and
obtain even better performance.Comment: Accepted in IEEE Transactions on Wireless Communication
Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization
In this paper, we propose an inexact block coordinate descent algorithm for
large-scale nonsmooth nonconvex optimization problems. At each iteration, a
particular block variable is selected and updated by inexactly solving the
original optimization problem with respect to that block variable. More
precisely, a local approximation of the original optimization problem is
solved. The proposed algorithm has several attractive features, namely, i) high
flexibility, as the approximation function only needs to be strictly convex and
it does not have to be a global upper bound of the original function; ii) fast
convergence, as the approximation function can be designed to exploit the
problem structure at hand and the stepsize is calculated by the line search;
iii) low complexity, as the approximation subproblems are much easier to solve
and the line search scheme is carried out over a properly constructed
differentiable function; iv) guaranteed convergence of a subsequence to a
stationary point, even when the objective function does not have a Lipschitz
continuous gradient. Interestingly, when the approximation subproblem is solved
by a descent algorithm, convergence of a subsequence to a stationary point is
still guaranteed even if the approximation subproblem is solved inexactly by
terminating the descent algorithm after a finite number of iterations. These
features make the proposed algorithm suitable for large-scale problems where
the dimension exceeds the memory and/or the processing capability of the
existing hardware. These features are also illustrated by several applications
in signal processing and machine learning, for instance, network anomaly
detection and phase retrieval
Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning
Phase retrieval aims at reconstructing unknown signals from magnitude
measurements of linear mixtures. In this paper, we consider the phase retrieval
with dictionary learning problem, which includes an additional prior
information that the measured signal admits a sparse representation over an
unknown dictionary. The task is to jointly estimate the dictionary and the
sparse representation from magnitude-only measurements. To this end, we study
two complementary formulations and develop efficient parallel algorithms by
extending the successive convex approximation framework using a smooth
majorization. The first algorithm is termed compact-SCAphase and is preferable
in the case of less diverse mixture models. It employs a compact formulation
that avoids the use of auxiliary variables. The proposed algorithm is highly
scalable and has reduced parameter tuning cost. The second algorithm, referred
to as SCAphase, uses auxiliary variables and is favorable in the case of highly
diverse mixture models. It also renders simple incorporation of additional side
constraints. The performance of both methods is evaluated when applied to blind
sparse channel estimation from subband magnitude measurements in a
multi-antenna random access network. Simulation results demonstrate the
efficiency of the proposed techniques compared to state-of-the-art methods.Comment: This work has been submitted to the IEEE Transactions on Signal
Processing for possible publication. Copyright may be transferred without
notice, after which this version may no longer be accessibl
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