24 research outputs found
A DCA-Like Algorithm and its Accelerated Version with Application in Data Visualization
In this paper, we present two variants of DCA (Different of Convex functions
Algorithm) to solve the constrained sum of differentiable function and
composite functions minimization problem, with the aim of increasing the
convergence speed of DCA. In the first variant, DCA-Like, we introduce a new
technique to iteratively modify the decomposition of the objective function.
This successive decomposition could lead to a better majorization and
consequently a better convergence speed than the basic DCA. We then incorporate
the Nesterov's acceleration technique into DCA-Like to give rise to the second
variant, named Accelerated DCA-Like. The convergence properties and the
convergence rate under Kudyka-Lojasiewicz assumption of both variants are
rigorously studied. As an application, we investigate our algorithms for the
t-distributed stochastic neighbor embedding. Numerical experiments on several
benchmark datasets illustrate the efficiency of our algorithms
A New Nonconvex Strategy to Affine Matrix Rank Minimization Problem
The affine matrix rank minimization (AMRM) problem is to find a matrix of
minimum rank that satisfies a given linear system constraint. It has many
applications in some important areas such as control, recommender systems,
matrix completion and network localization. However, the problem (AMRM) is
NP-hard in general due to the combinational nature of the matrix rank function.
There are many alternative functions have been proposed to substitute the
matrix rank function, which lead to many corresponding alternative minimization
problems solved efficiently by some popular convex or nonconvex optimization
algorithms. In this paper, we propose a new nonconvex function, namely,
function (with ), to
approximate the rank function, and translate the NP-hard problem (AMRM) into
the function affine matrix rank minimization (TLAMRM)
problem. Firstly, we study the equivalence of problem (AMRM) and (TLAMRM), and
proved that the uniqueness of global minimizer of the problem (TLAMRM) also
solves the NP-hard problem (AMRM) if the linear map satisfies a
restricted isometry property (RIP). Secondly, an iterative thresholding
algorithm is proposed to solve the regularization problem (RTLAMRM) for all
. At last, some numerical results on low-rank
matrix completion problems illustrated that our algorithm is able to recover a
low-rank matrix, and the extensive numerical on image inpainting problems shown
that our algorithm performs the best in finding a low-rank image compared with
some state-of-art methods
Pinball Loss Minimization for One-bit Compressive Sensing: Convex Models and Algorithms
The one-bit quantization is implemented by one single comparator that
operates at low power and a high rate. Hence one-bit compressive sensing
(1bit-CS) becomes attractive in signal processing. When measurements are
corrupted by noise during signal acquisition and transmission, 1bit-CS is
usually modeled as minimizing a loss function with a sparsity constraint. The
one-sided loss and the linear loss are two popular loss functions for
1bit-CS. To improve the decoding performance on noisy data, we consider the
pinball loss, which provides a bridge between the one-sided loss and
the linear loss. Using the pinball loss, two convex models, an elastic-net
pinball model and its modification with the -norm constraint, are
proposed. To efficiently solve them, the corresponding dual coordinate ascent
algorithms are designed and their convergence is proved. The numerical
experiments confirm the effectiveness of the proposed algorithms and the
performance of the pinball loss minimization for 1bit-CS.Comment: 11 page
Projection Neural Network for a Class of Sparse Regression Problems with Cardinality Penalty
In this paper, we consider a class of sparse regression problems, whose
objective function is the summation of a convex loss function and a cardinality
penalty. By constructing a smoothing function for the cardinality function, we
propose a projected neural network and design a correction method for solving
this problem. The solution of the proposed neural network is unique, global
existent, bounded and globally Lipschitz continuous. Besides, we prove that all
accumulation points of the proposed neural network have a common support set
and a unified lower bound for the nonzero entries. Combining the proposed
neural network with the correction method, any corrected accumulation point is
a local minimizer of the considered sparse regression problem. Moreover, we
analyze the equivalent relationship on the local minimizers between the
considered sparse regression problem and another regression sparse problem.
Finally, some numerical experiments are provided to show the efficiency of the
proposed neural networks in solving some sparse regression problems in
practice
Sparse Bayesian Inference of Multivariable ARX Networks
Increasing attention has recently been given to the inference of sparse
networks. In biology, for example, most molecules only bind to a small number
of other molecules, leading to sparse molecular interaction networks. To
achieve sparseness, a common approach consists of applying weighted penalties
to the number of links between nodes in the network and the complexity of the
dynamics of existing links. The selection of proper weights, however, is
non-trivial. Alternatively, this paper proposes a novel data-driven method,
called GESBL, that is able to penalise both network sparsity and model
complexity without any tuning. GESBL combines Sparse Bayesian Learning (SBL)
and Group Sparse Bayesian Learning (GSBL) to introduce penalties for
complexity, both in terms of element (system order of nonzero connections) and
group sparsity (network topology). The paper considers a class of sparse linear
time-invariant networks where the dynamics are represented by multivariable ARX
models. Data generated from sparse random ARX networks and synthetic gene
regulatory networks indicate that our method, on average, considerably
outperforms existing state-of-the-art methods. The proposed method can be
applied to a wide range of fields, from systems biology applications in
signalling and genetic regulatory networks to power systems
Alternating Direction Method of Multipliers for Truss Topology Optimization with Limited Number of Nodes: A Cardinality-Constrained Second-Order Cone Programming Approach
This paper addresses the compliance minimization of a truss, where the number
of available nodes is limited. It is shown that this optimization problem can
be recast as a second-order cone programming with a cardinality constraint. We
propose a simple heuristic based on the alternative direction method of
multipliers. The efficiency of the proposed method is compared with a global
optimization approach based on mixed-integer second-order cone programming.
Numerical experiments demonstrate that the proposed method often finds a
solution having a good objective value with small computational cost
Uncoded Placement Optimization for Coded Delivery
We consider the classical coded caching problem as defined by Maddah-Ali and
Niesen, where a server with a library of files of equal size is connected
to users via a shared error-free link. Each user is equipped with a cache
with capacity of files. The goal is to design a static content placement
and delivery scheme such that the average load over the shared link is
minimized. We first present a class of centralized coded caching schemes
consisting of a general content placement strategy specified by a file
partition parameter, enabling efficient and flexible content placement, and a
specific content delivery strategy, enabling load reduction by exploiting
common requests of different users. For the proposed class of schemes, we
consider two cases for the optimization of the file partition parameter,
depending on whether a large subpacketization level is allowed or not. In the
case of an unrestricted subpacketization level, we formulate the coded caching
optimization in order to minimize the average load under an arbitrary file
popularity. A direct formulation of the problem involves variables. By
imposing some additional conditions, the problem is reduced to a linear program
with variables under an arbitrary file popularity and with
variables under the uniform file popularity. We can recover Yu {\em et al.}'s
optimal scheme for the uniform file popularity as an optimal solution of our
problem. When a low subpacketization level is desired, we introduce a
subpacketization level constraint involving the norm for each file.
Again, by imposing the same additional conditions, we can simplify the problem
to a difference of two convex functions (DC) problem with variables
that can be efficiently solved.Comment: 30 pages, 8 figures, presented in part at IEEE WiOpt 201
Bandwidth Gain from Mobile Edge Computing and Caching in Wireless Multicast Systems
In this paper, we present a novel mobile edge computing (MEC) model where the
MEC server has the input and output data of all computation tasks and
communicates with multiple caching-and-computing-enabled mobile devices via a
shared wireless link. Each task request can be served from local output
caching, local computing with input caching, local computing or MEC computing,
each of which incurs a unique bandwidth requirement of the multicast link.
Aiming to minimize the transmission bandwidth, we design and optimize the local
caching and computing policy at mobile devices subject to latency, caching,
energy and multicast transmission constraints. The joint policy optimization
problem is shown to be NP-hard. When the output data size is smaller than the
input data size, we reformulate the problem as minimization of a monotone
submodular function over matroid constraints and obtain the optimal solution
via a strongly polynomial algorithm of Schrijver. On the other hand, when the
output data size is larger than the input data size, by leveraging sample
approximation and concave convex procedure together with the alternating
direction method of multipliers, we propose a low-complexity high-performance
algorithm and prove it converges to a stationary point. Furthermore, we
theoretically reveal how much bandwidth gain can be achieved from computing and
caching resources at mobile devices or the multicast transmission for symmetric
case. Our results indicate that exploiting the computing and caching resources
at mobile devices as well as multicast transmission can provide significant
bandwidth savings.Comment: submitted to IEEE Trans. Wireless Communications. arXiv admin note:
text overlap with arXiv:1807.0553
Content-Centric Sparse Multicast Beamforming for Cache-Enabled Cloud RAN
This paper presents a content-centric transmission design in a cloud radio
access network (cloud RAN) by incorporating multicasting and caching. Users
requesting a same content form a multicast group and are served by a same
cluster of base stations (BSs) cooperatively. Each BS has a local cache and it
acquires the requested contents either from its local cache or from the central
processor (CP) via backhaul links. We investigate the dynamic content-centric
BS clustering and multicast beamforming with respect to both channel condition
and caching status. We first formulate a mixed-integer nonlinear programming
problem of minimizing the weighted sum of backhaul cost and transmit power
under the quality-of-service constraint for each multicast group. Theoretical
analysis reveals that all the BSs caching a requested content can be included
in the BS cluster of this content, regardless of the channel conditions. Then
we reformulate an equivalent sparse multicast beamforming (SBF) problem. By
adopting smoothed -norm approximation and other techniques, the SBF
problem is transformed into the difference of convex (DC) programs and
effectively solved using the convex-concave procedure algorithms. Simulation
results demonstrate significant advantage of the proposed content-centric
transmission. The effects of three heuristic caching strategies are also
evaluated.Comment: To appear in IEEE Trans. on Wireless Communication
Modeling and Trade-off for Mobile Communication, Computing and Caching Networks
Computation task service delivery in a computing-enabled and caching-aided
multi-user mobile edge computing (MEC) system is studied in this paper, where a
MEC server can deliver the input or output datas of tasks to mobile devices
over a wireless multicast channel. The computing-enabled and caching-aided
mobile devices are able to store the input or output datas of some tasks, and
also compute some tasks locally, reducing the wireless bandwidth consumption.
The corresponding framework of this system is established, and under the
latency constraint, we jointly optimize the caching and computing policy at
mobile devices to minimize the required transmission bandwidth. The joint
policy optimization problem is shown to be NP-hard, and based on equivalent
transformation and exact penalization of the problem, a stationary point is
obtained via concave convex procedure (CCCP). Moreover, in a symmetric
scenario, gains offered by this approach are derived to analytically understand
the influences of caching and computing resources at mobile devices, multicast
transmission, the number of mobile devices, as well as the number of tasks on
the transmission bandwidth. Our results indicate that exploiting the computing
and caching resources at mobile devices can provide significant bandwidth
savings.Comment: to appear in IEEE GLOBECOM 201