Showing papers on "Convergence (routing) published in 2010"
TL;DR: It is shown that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence large scale TTD problems can be efficiently solved by the proposed method.
Abstract: We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions. Under appropriate conditions, a monotone convergence to a KKT point is established. The scheme is applied to truss topology design (TTD) problems, where the nonconvex constraints are associated with bounds on displacements and stresses. It is shown that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence large scale TTD problems can be efficiently solved by the proposed method.
551 citations
Proceedings Article•
06 Dec 2010TL;DR: Singular value projection (SVP) as discussed by the authors is a simple and fast algorithm for rank minimization under affine constraints (ARMP) and shows that SVP recovers the minimum rank solution for affine constraint that satisfy a restricted isometry property (RIP).
Abstract: Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization under affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy a restricted isometry property (RIP). Our method guarantees geometric convergence rate even in the presence of noise and requires strictly weaker assumptions on the RIP constants than the existing methods. We also introduce a Newton-step for our SVP framework to speed-up the convergence with substantial empirical gains. Next, we address a practically important application of ARMP - the problem of low-rank matrix completion, for which the defining affine constraints do not directly obey RIP, hence the guarantees of SVP do not hold. However, we provide partial progress towards a proof of exact recovery for our algorithm by showing a more restricted isometry property and observe empirically that our algorithm recovers low-rank incoherent matrices from an almost optimal number of uniformly sampled entries. We also demonstrate empirically that our algorithms outperform existing methods, such as those of [5, 18, 14], for ARMP and the matrix completion problem by an order of magnitude and are also more robust to noise and sampling schemes. In particular, results show that our SVP-Newton method is significantly robust to noise and performs impressively on a more realistic power-law sampling scheme for the matrix completion problem.
445 citations
TL;DR: Based on the concept of control topology, an impulsive controller is designed to achieve the exponential synchronization of CDNs, and moreover, the exponential convergence rate can be specified.
Abstract: In this paper, the synchronization of complex dynamical networks (CDNs) with system delay and multiple coupling delays is studied via impulsive distributed control. The concept of control topology is introduced to describe the whole controller structure, which consists of some directed connections between nodes. The control topology can be designed either to be the same as the non-delayed coupling topology of the network, or to be independent of the intrinsic network topology. Based on the concept of control topology, an impulsive controller is designed to achieve the exponential synchronization of CDNs, and moreover, the exponential convergence rate can be specified. Illustrated examples have been given to show the effectiveness of the proposed impulsive distributed control strategy.
395 citations
TL;DR: The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions and is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem.
291 citations
TL;DR: A rendezvous protocol with double-integrator dynamics is proposed, which can enable the group of mobile agents to converge to the same position and move with the same velocity while preserving the connectivity of the whole network during the evolution if the initial network is connected.
270 citations
TL;DR: In this paper, a unified framework for establishing consistency and convergence rates for regularized M-estimators under high-dimensional scaling was provided, which can be used to re-derive some existing results.
Abstract: High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a line of recent work has studied models with various types of low-dimensional structure, including sparse vectors, sparse and structured matrices, low-rank matrices and combinations thereof. In such settings, a general approach to estimation is to solve a regularized optimization problem, which combines a loss function measuring how well the model fits the data with some regularization function that encourages the assumed structure. This paper provides a unified framework for establishing consistency and convergence rates for such regularized M-estimators under high-dimensional scaling. We state one main theorem and show how it can be used to re-derive some existing results, and also to obtain a number of new results on consistency and convergence rates, in both $\ell_2$-error and related norms. Our analysis also identifies two key properties of loss and regularization functions, referred to as restricted strong convexity and decomposability, that ensure corresponding regularized M-estimators have fast convergence rates and which are optimal in many well-studied cases.
243 citations
30 Aug 2010
TL;DR: This paper designs an extended routing service allowing easy implementation of application-specific routing protocols on CamCube, and demonstrates the benefits and network-level impact of running multiple routing protocols.
Abstract: Building distributed applications that run in data centers is hard. The CamCube project explores the design of a shipping container sized data center with the goal of building an easier platform on which to build these applications. CamCube replaces the traditional switch-based network with a 3D torus topology, with each server directly connected to six other servers. As in other proposals, e.g. DCell and BCube, multi-hop routing in CamCube requires servers to participate in packet forwarding. To date, as in existing data centers, these approaches have all provided a single routing protocol for the applications.In this paper we explore if allowing applications to implement their own routing services is advantageous, and if we can support it efficiently. This is based on the observation that, due to the flexibility offered by the CamCube API, many applications implemented their own routing protocol in order to achieve specific application-level characteristics, such as trading off higher-latency for better path convergence. Using large-scale simulations we demonstrate the benefits and network-level impact of running multiple routing protocols. We demonstrate that applications are more efficient and do not generate additional control traffic overhead. This motivates us to design an extended routing service allowing easy implementation of application-specific routing protocols on CamCube. Finally, we demonstrate that the additional performance overhead incurred when using the extended routing service on a prototype CamCube is very low.
242 citations
15 Mar 2010
TL;DR: A novel network-level strategy based on a modification of current link-state routing protocols, such as OSPF, is proposed; according to this strategy, IP routers are able to power off some network links during low traffic periods.
Abstract: In this paper we analyze the challenging problem of energy saving in IP networks. A novel network-level strategy based on a modification of current link-state routing protocols, such as OSPF, is proposed; according to this strategy, IP routers are able to power off some network links during low traffic periods. The proposed solution is a three-phases algorithm: in the first phase some routers are elected as "exporter" of their own Shortest Path Trees (SPTs); in the second one the neighbors of these routers perform a modified Dijkstra algorithm to detect links to power off; in the last one new network paths on a modified network topology are computed. Performance study shows that, in an actual IP network, even more than the 60% of links can be switched off.
200 citations
TL;DR: Under weak observability conditions the authors prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process.
Abstract: This paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation. Under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process. Simulation examples are provided in order to show the main features of the proposed method.
194 citations
TL;DR: A novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts and the FC demonstrates a potential for interpreting evolution of the algorithm and to control its convergence.
Abstract: This paper proposes a novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts. The optimization is tested for several well-known functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed. The FC demonstrates a potential for interpreting evolution of the algorithm and to control its convergence.
191 citations
TL;DR: An alternative approach of the variational iteration method is presented, then the convergence of the method for nonlinear differential equations is studied to address the sufficient condition for convergence and the error estimate.
TL;DR: The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square type distributed adaptive filters with colored inputs to achieve an acceptable misadjustment performance with lower computational and memory cost.
Abstract: We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton's method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.
TL;DR: The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions, validate the proposed convergence theorem and indicate that this ARX-like model contains a characteristic polynomial and differs from the conventional multivariable ARX system.
Abstract: This paper studies the convergence of the stochastic gradient identification algorithm of multi-input multi-output ARX-like systems (i.e., multivariable ARX-like systems) by using the stochastic martingale theory. This ARX-like model contains a characteristic polynomial and differs from the conventional multivariable ARX system. The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions. The simulation results validate the proposed convergence theorem.
TL;DR: This paper study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter finds that there is an optimal value of the shape parameters for which the error is minimum.
TL;DR: Small-sample validity of the statistical test and ranking-and-selection procedure is proven for normally distributed data, and ISC is compared to the commercial optimization via simulation package OptQuest on five test problems that range from 2 to 20 decision variables and on the order of 104 to 1020 feasible solutions.
Abstract: Industrial Strength COMPASS (ISC) is a particular implementation of a general framework for optimizing the expected value of a performance measure of a stochastic simulation with respect to integer-ordered decision variables in a finite (but typically large) feasible region defined by linear-integer constraints. The framework consists of a global-search phase, followed by a local-search phase, and ending with a “clean-up” (selection of the best) phase. Each phase provides a probability 1 convergence guarantee as the simulation effort increases without bound: Convergence to a globally optimal solution in the global-search phase; convergence to a locally optimal solution in the local-search phase; and convergence to the best of a small number of good solutions in the clean-up phase. In practice, ISC stops short of such convergence by applying an improvement-based transition rule from the global phase to the local phase; a statistical test of convergence from the local phase to the clean-up phase; and a ranking-and-selection procedure to terminate the clean-up phase. Small-sample validity of the statistical test and ranking-and-selection procedure is proven for normally distributed data. ISC is compared to the commercial optimization via simulation package OptQuest on five test problems that range from 2 to 20 decision variables and on the order of 104 to 1020 feasible solutions. These test cases represent response-surface models with known properties and realistic system simulation problems.
TL;DR: This work considers a distributed average consensus algorithm over a network in which communication links fail with independent probability and gives expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks.
Abstract: We consider a distributed average consensus algorithm over a network in which communication links fail with independent probability. In such stochastic networks, convergence is defined in terms of the variance of deviation from average. We first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures. We then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise. We give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks. We also present simulation-free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability.
TL;DR: This paper proposes fractional-order formation control algorithms with absolute/relative damping and studies the conditions on the network topology and the control gains such that the formation control will be achieved under a directed fixed networkTopology.
TL;DR: Compared to typical routing algorithms in sensor networks and the traditional ant-based algorithm, this new algorithm has better convergence and provides significantly better QoS for multiple types of services in wireless multimedia sensor networks.
TL;DR: This research investigates distributed clustering scheme and proposes a cluster-based routing protocol for Delay-Tolerant Mobile Networks (DTMNs), showing that it achieves higher delivery ratio and significantly lower overhead and end-to-end delay compared with its non-clustering counterpart.
Abstract: This research investigates distributed clustering scheme and proposes a cluster-based routing protocol for Delay-Tolerant Mobile Networks (DTMNs). The basic idea is to distributively group mobile nodes with similar mobility pattern into a cluster, which can then interchangeably share their resources (such as buffer space) for overhead reduction and load balancing, aiming to achieve efficient and scalable routing in DTMN. Due to the lack of continuous communications among mobile nodes and possible errors in the estimation of nodal contact probability, convergence and stability become major challenges in distributed clustering in DTMN. To this end, an exponentially weighted moving average (EWMA) scheme is employed for on-line updating nodal contact probability, with its mean proven to converge to the true contact probability. Based on nodal contact probabilities, a set of functions including Sync(), Leave(), and Join() are devised for cluster formation and gateway selection. Finally, the gateway nodes exchange network information and perform routing. Extensive simulations are carried out to evaluate the effectiveness and efficiency of the proposed cluster-based routing protocol. The simulation results show that it achieves higher delivery ratio and significantly lower overhead and end-to-end delay compared with its non-clustering counterpart.
TL;DR: A measurement model with a random link gain, additive noise, and Markovian lossy signal reception, which captures uncertain operational conditions of practical networks is proposed and a common stochastic Lyapunov function technique is used to prove convergence.
TL;DR: For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values.
Abstract: This paper is concerned with the numerical solutions to the linear matrix equations A"1XB"1=F"1 and A"2XB"2=F"2; two iterative algorithms are presented to obtain the solutions. For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values. Finally, simulation examples are given to verify the proposed convergence theorems.
TL;DR: This work proposes the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change and incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS), and two other MOEAs for dynamic optimization.
Abstract: An essential feature of a dynamic multiobjective evolutionary algorithm (MOEA) is to converge quickly to the Pareto-optimal Set before it changes. In cases where the behavior of the dynamic problem follows a certain trend, convergence can be accelerated by anticipating the characteristics of future changes in the problem. A prediction model is usually used to exploit past information and estimate the location of the new Pareto-optimal Set. In this work, we propose the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change. The predicted direction and magnitude of the next change, known as the predictive gradient, is estimated based on the history of previously discovered solutions using a weighted average approach. Solutions updated with the predictive gradient will remain in the vicinity of the new Pareto-optimal Set and help the rest of the population to converge. The prediction strategy is simple to implement, making it suitable for fast-changing problems. In addition, a new memory technique is introduced to exploit any periodicity in the dynamic problem. The memory technique selects only the more promising stored solutions for retrieval in order to reduce the number of evaluations used. Both techniques are incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS) and two other MOEAs for dynamic optimization and results indicate that they are effective at improving performance on several dynamic multiobjective test problems.
TL;DR: In this paper, a homotopy analysis based method was developed for the solution of nonlinear ordinary differential equations of fractional order, and the proposed algorithm presented the procedure of constructing the set of base functions and gave the high-order deformation equation in a simple form.
TL;DR: In this article, the authors develop and analyze distributed algorithms based on dual averaging of subgradients, and provide sharp bounds on their convergence rates as a function of the network size and topology.
Abstract: The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.
TL;DR: A flaw in the original PSO is identified which causes stagnation of the swarm, Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum and further extensions with provable global convergence are described.
Abstract: The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.
07 Oct 2010
TL;DR: This paper presents a new multiplicative algorithm for nonnegative matrix factorization with β-divergence, theoretically proven for any real-valued β based on the auxiliary function method.
Abstract: This paper presents a new multiplicative algorithm for nonnegative matrix factorization with β-divergence. The derived update rules have a similar form to those of the conventional multiplicative algorithm, only differing through the presence of an exponent term depending on β. The convergence is theoretically proven for any real-valued β based on the auxiliary function method. The convergence speed is experimentally investigated in comparison with previous works.
01 Dec 2010
TL;DR: This work develops an alternative distributed Newton-type fast converging algorithm for solving network utility maximization problems with self-concordant utility functions by using novel matrix splitting techniques and shows that even when the Newton direction and the stepsize in this method are computed within some error, the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood.
Abstract: Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newton-type fast converging algorithm for solving network utility maximization problems with self-concordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes in a decentralized manner with limited scalar information exchange. Similarly, the stepsize can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the stepsize in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition.
TL;DR: In this paper, a nonlinear adaptive controller is designed that yields convergence of the trajectories of the closed-loop system to the path in the presence of constant unknown ocean currents and parametric model uncertainty.
Abstract: This paper addresses the problem of cooperative path-following of multiple autonomous vehicles. Stated briefly, the problem consists of steering a group of vehicles along specified paths while keeping a desired spatial formation. For a given class of autonomous surface vessels, it is shown how Lyapunov-based techniques and graph theory can be brought together to design a decentralized control structure, where the vehicle dynamics and the constraints imposed by the topology of the inter-vehicle communication network are explicitly taken into account. To achieve path-following for each vehicle, a nonlinear adaptive controller is designed that yields convergence of the trajectories of the closed-loop system to the path in the presence of constant unknown ocean currents and parametric model uncertainty. The controller derived implicitly compensates for the effect of the ocean current without the need for direct measurements of its velocity. Vehicle cooperation is achieved by adjusting the speed of each vehicle along its path according to information exchanged on the positions of a subset of the other vehicles, as determined by the communication topology adopted. Global stability and convergence of the closed-loop system are guaranteed. Illustrative examples are presented and discussed. Copyright © 2009 John Wiley & Sons, Ltd.
TL;DR: In this article, a parametric level-set approach was used to represent flow boundaries, resulting in a non-trivial mapping between design variables and local material properties, and the performance of the level set approach was compared to a traditional material distribution approach.
Abstract: Traditional methods based on an element-wise parameterization of the material distribution applied to the topology optimization of fluidic systems often suffer from slow convergence of the optimization process, as well as robustness issues at increased Reynolds numbers. The local influence of the design variables in the traditional approaches is seen as a possible cause for the slow convergence. Non-smooth material distributions are suspected to trigger premature onset of instationary flows which cannot be treated by steady-state flow models. In the present work, we study whether the convergence and the versatility of topology optimization methods for fluidic systems can be improved by employing a parametric level-set description. In general, level-set methods allow controlling the smoothness of boundaries, yield a non-local influence of design variables, and decouple the material description from the flow field discretization. The parametric level-set method used in this study utilizes a material distribution approach to represent flow boundaries, resulting in a non-trivial mapping between design variables and local material properties. Using a hydrodynamic lattice Boltzmann method, we study the performance of our level-set approach in comparison to a traditional material distribution approach. By numerical examples, the parametric level-set approach is validated through comparison with traditional material distribution based methods. While the parametric level-set approach leads to similar optimal designs, the present study reveals no general improvements of the convergence of the optimization process and of the robustness of the nonlinear flow analyses when compared to the traditional material distribution approach. Instead, our numerical experiment suggests that a continuation method operating on the volume constraint is needed to achieve optimal designs at higher Reynolds numbers.