Primal-dual Decomposition Method Research Articles

Cache Replacement Strategy With Limited Service Capacity in Heterogeneous Networks

Recently, cellular networks face a huge challenge to satisfy large increment of user demands for higher-speed and lower-latency communication service. One promising solution is to apply the cache technology in edge cache networks to reduce redundant data transmission. The cache technology is effective, but the cache capacity is limited. Researchers have proposed various cache strategies to efficiently utilize the limited cache capacity. However, most existing solutions have not taken into account the service capacity limitation of mobile devices. In this paper, we propose a cache replacement strategy for heterogeneous networks considering the limitation of service capacity and user mobility. In the cache replacement strategy, we utilize the user characteristics, such as user mobility and file popularity, to estimate the user demands, and then define the system cost. We formulate the cache strategy design as a mixed integer linear programming problem to minimize the system cost, and use Lagrangian relaxation and hierarchical primal-dual decomposition method to solve this problem. Numerical results show that the proposed cache strategy can significantly reduce the system cost and increase the cache hit ratio compared to the cache strategy that does not consider the limitation of user service capacity.

Unified Distributed Control of Stand-Alone DC Microgrids

Stand-alone direct current (dc) microgrids may belong to different owners and adopt various control strategies. This brings great challenge to its optimal operation due to the difficulty of implementing a unified control. This paper addresses the distributed optimal control of dc microgrids, which intends to break the restriction of diversity to some extent. First, we formulate the optimal power flow problem of stand-alone dc microgrids as an exact second-order cone program and prove the uniqueness of the optimal solution. Then a dynamic solving algorithm based on primal–dual decomposition method is proposed, the convergence of which is proved theoretically as well as the optimality of its equilibrium point. It should be stressed that the algorithm can provide control commands for the three types of microgrids: 1) power control; 2) voltage control; and 3) droop control. This implies that each microgrid does not need to change its original control strategy in practice, which is less influenced by the diversity of microgrids. Moreover, the control commands for power controlled and voltage controlled microgrids satisfy generation limits and voltage limits in both transient process and steady state. Finally, a six-microgrid dc system based on the microgrid benchmark is adopted to validate the effectiveness and plug-n-play property of our designs.

Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software-Defined Networks

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path fair resource allocation problem in a distributed SDN control architecture. Our ADMM-based algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances at scale.

Optimal Cooperative Content Caching and Delivery Policy for Heterogeneous Cellular Networks

To address the explosively growing demand for mobile data services in the 5th generation (5G) mobile communication system, it is important to develop efficient content caching and distribution techniques, aiming at significantly reducing redundant data transmissions and improving content delivery efficiency. In heterogeneous cellular network (HetNet), which has been deemed as a promising architectural technique for 5G, caching some popular content items at femto base-stations (FBSs) and even at user equipment (UE) can be exploited to alleviate the burden of backhaul and to reduce the costly transmissions from the macro base-stations to UEs. In this paper, we develop the optimal cooperative content caching and delivery policy, for which FBSs and UEs are all engaged in local content caching. We formulate the cooperative content caching problem as an integer-linear programming problem, and use hierarchical primal-dual decomposition method to decouple the problem into two level optimization problems, which are solved by using the subgradient method. Furthermore, we design the optimal content delivery policy, which is formulated as an unbalanced assignment problem and solved by using Hungarian algorithm. Numerical results have shown that the proposed cooperative content caching and delivery policy can significantly improve content delivery performance in comparison with existing caching strategies.

A Column Generation Method for Constructing and Scheduling Multiple Forwarding Trees in Wireless Sensor Networks

This paper considers the problem of jointly constructing and scheduling forwarding trees in a wireless sensor network, each to collect measurements from a group of sensor nodes at a single sink node. The goal is to construct such trees that gather measurements in the most energy efficient manner and with minimal gathering latency. We assume transmissions (carrying measurements) on wireless links interfere with one another, and thus, appropriate link scheduling is required to manage interference. We refer to this problem as forwarding tree construction and scheduling (FTCS). Each tree may be constructed independently, and then, its links are scheduled. However, when all trees are combined together, the shortest and energy efficient schedule may not be guaranteed. Furthermore, a large number of possible forwarding trees for each group of sensors may be considered. Both problems of enumerating forwarding trees and scheduling links for those trees are hard combinatorial problems. This is compounded by the fact that the two problems must be solved jointly, to guarantee the selection of the best forwarding trees that, when their links are scheduled, guarantee a shortest energy efficient schedule. After highlighting the complexity of the FTCS problem, we present a novel primal-dual decomposition method using column generation. We also highlight several challenges we faced when solving the decomposed problem and present efficient techniques for mitigating those challenges. One major advantage of this paper is that it can serve as a benchmark for evaluating the performance of any low complexity method for solving the FTCS problem for larger network instances, where no known exact solutions can be found.

Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Flexible strategies are used to select the blocks of operators activated at each iteration. In addition, we allow lags in operator processing, permitting asynchronous implementation. The decomposition phase of each iteration of our methods is to generate points in the graphs of the selected monotone operators, in order to construct a half-space containing the Kuhn–Tucker set associated with the system. The coordination phase of each iteration involves a projection onto this half-space. We present two related methods: the first method provides weakly convergent primal and dual sequences under general conditions, while the second is a variant in which strong convergence is guaranteed without additional assumptions. Neither algorithm requires prior knowledge of bounds on the linear operators involved or the inversion of linear operators. Our algorithmic framework unifies and significantly extends the approaches taken in earlier work on primal-dual projective splitting methods.

A practical approach for outdoors distributed target localization in wireless sensor networks

Wireless sensor networks are posed as the new communication paradigm where the use of small, low-complexity, and low-power devices is preferred over costly centralized systems. The spectra of potential applications of sensor networks is very wide, ranging from monitoring, surveillance, and localization, among others. Localization is a key application in sensor networks and the use of simple, efficient, and distributed algorithms is of paramount practical importance. Combining convex optimization tools with consensus algorithms we propose a distributed localization algorithm for scenarios where received signal strength indicator readings are used. We approach the localization problem by formulating an alternative problem that uses distance estimates locally computed at each node. The formulated problem is solved by a relaxed version using semidefinite relaxation technique. Conditions under which the relaxed problem yields to the same solution as the original problem are given and a distributed consensus-based implementation of the algorithm is proposed based on an augmented Lagrangian approach and primal-dual decomposition methods. Although suboptimal, the proposed approach is very suitable for its implementation in real sensor networks, i.e., it is scalable, robust against node failures and requires only local communication among neighboring nodes. Simulation results show that running an additional local search around the found solution can yield performance close to the maximum likelihood estimate.

Optimal Flexible Spectrum Access in Wireless Networks with Software Defined Radios

We investigate the problem of flexible spectrum access in multihop wireless networks. We assume radios that are capable of transmitting on channels of contiguous frequency bands and which do not require any sophisticated processing. Because these radios can flexibly configure their transmissions anywhere in the available frequency band, the spectrum becomes vulnerable to fragmentation and interference. We consider the joint problem of routing, link scheduling and spectrum allocation where scheduling feasibility is considered under the physical interference (SINR) constraint. We present a primal-dual decomposition for this complex optimization problem based on column generation. We show that obtaining the optimal solution to this problem is computationally not feasible, except for very small networks. We thus adopt a two-fold method to circumvent the complexity while yielding practical solutions. First, we relax the SINR constraint and use a simplified graph-based model for the interference. Second, we use a simulated annealing (SA) approach to solve the dual subproblem. Our SA approach however is augmented with an SINR feasibility check. Our results confirm that the primal-dual decomposition method using SA substantially reduces the computation time and achieves near optimal solutions. The results also reveal that substantial improvement in network performance is obtained with flexible spectrum assignment which results from its capability of better managing the interference in the network.

Resource Allocation for Error Resilient Video Coding Over AWGN Using Optimization Approach

The number of slices for error resilient video coding is jointly optimized with 802.11a-like media access control and the physical layers with automatic repeat request and rate compatible punctured convolutional code over additive white gaussian noise channel as well as channel times allocation for time division multiple access. For error resilient video coding, the relation between the number of slices and coding efficiency is analyzed and formulated as a mathematical model. It is applied for the joint optimization problem, and the problem is solved by a convex optimization method such as the primal-dual decomposition method. We compare the performance of a video communication system which uses the optimal number of slices with one that codes a picture as one slice. From numerical examples, end-to-end distortion of utility functions can be significantly reduced with the optimal slices of a picture especially at low signal-to-noise ratio.

Resource Allocation for TDMA Video Commtmmunication Over AWGN Using Cross-Layer Optimization Approach

Cross-layer optimization approach is applied to allocate channel times of time-division multiple access (TDMA) to utility functions which send different video streams with different rate-distortion characteristics. Given a channel time, each utility function solves an optimization problem to obtain the optimal source code rate, channel code rate and media access control (MAC) frame size. In this paper, we derive mathematical models to represent end-to-end distortion of video streams and 802.11a-like MAC and PHY with automatic repeat reQuest (ARQ) and rate compatible punctured convolutional code (RCPC) over additive white Gaussian noise (AWGN) channel. These models are formulated as a convex optimization problem, and it is solved by the primal-dual decomposition method. In addition, coexistence among the proposed utility functions and conventional utility functions is discussed. Finally, numerical examples show that significant reduction of overall distortion of utility functions can be achieved.

Mean value cross decomposition for nonlinear convex problems

Mean value cross decomposition is a symmetric primal–dual decomposition method suitable for optimization problems with both primal and dual structures. It uses only easily solvable subproblems and no difficult master problems. Originally developed for linear problems, it is in this paper extended to nonlinear convex optimization problems. Convergence is proved for a somewhat generalized version, allowing more general weights. Computational results are presented for a network routing problem with congestion costs, a large-scale nonlinear problem with structures that enable decomposition both with respect to variables and constraints. The main goals of the tests are to illustrate the procedure and to indicate that this decomposition approach is more efficient than direct solution with a well established general code.

Applications of the method of partial inverses to convex programming: Decomposition

A primal–dual decomposition method is presented to solve the separable convex programming problem. Convergence to a solution and Lagrange multiplier vector occurs from an arbitrary starting point. The method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction. In the nonseparable case, it specializes to a known method, the proximal method of multipliers. Conditions are provided which guarantee linear convergence.