Showing papers on "Convergence (routing) published in 2004"

Quantum-inspired evolutionary algorithms with a new termination criterion, H/sub /spl epsi// gate, and two-phase scheme

Abstract: From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.

Gamma-convergence of gradient flows with applications to Ginzburg-Landau

Abstract: We present a method to prove convergence of gradient flows of families of energies that Γ-converge to a limiting energy. It provides lower-bound criteria to obtain the convergence that correspond to a sort of C1-order Γ-convergence of functionals. We then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the Ginzburg-Landau energy in dimension 2, retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field. © 2004 Wiley Periodicals, Inc.

An adaptive notch filter for frequency estimation of a periodic signal

Abstract: Online frequency estimation of a pure sinusoidal signal is a classical problem that has many practical applications. Recently an ANF with global convergence property has been developed for this purpose. There exist some practical applications in which signals are not pure sinusoidal and contain harmonics. Therefore, online frequency estimation of periodic but not necessarily sinusoidal signals espoused by such applications becomes quite important. This note presents an alternative stability analysis for a modified ANF that permits the presence of harmonics in the incoming signal. Also, this stability analysis is simpler and alleviates the problem complexity even in the case of pure sinusoidal signal. Simulation results confirm theoretical issues.

On the convergence of a class of estimation of distribution algorithms

Abstract: We investigate the global convergence of estimation of distribution algorithms (EDAs). In EDAs, the distribution is estimated from a set of selected elements, i.e., the parent set, and then the estimated distribution model is used to generate new elements. In this paper, we prove that: 1) if the distribution of the new elements matches that of the parent set exactly, the algorithms will converge to the global optimum under three widely used selection schemes and 2) a factorized distribution algorithm converges globally under proportional selection.

Dynamics of hot-potato routing in IP networks

Abstract: Despite the architectural separation between intradomain and interdomain routing in the Internet, intradomain protocols do influence the path-selection process in the Border Gateway Protocol (BGP). When choosing between multiple equally-good BGP routes, a router selects the one with the closest egress point, based on the intradomain path cost. Under such hot-potato routing, an intradomain event can trigger BGP routing changes. To characterize the influence of hot-potato routing, we conduct controlled experiments with a commercial router. Then, we propose a technique for associating BGP routing changes with events visible in the intradomain protocol, and apply our algorithm to AT&T's backbone network. We show that (i) hot-potato routing can be a significant source of BGP updates, (ii) BGP updates can lag 60 seconds or more behind the intradomain event, (iii) the number of BGP path changes triggered by hot-potato routing has a nearly uniform distribution across destination prefixes, and (iv) the fraction of BGP messages triggered by intradomain changes varies significantly across time and router locations. We show that hot-potato routing changes lead to longer delays in forwarding-plane convergence, shifts in the flow of traffic to neighboring domains, extra externally-visible BGP update messages, and inaccuracies in Internet performance measurements.

Multiscale Finite Element Methods for Nonlinear Problems and Their Applications

Abstract: In this paper we propose a generalization of multiscale finite element methods (Ms-FEM) to nonlinear problems. We study the convergence of the proposed method for nonlinear elliptic equations and propose an oversampling technique. Numerical examples demonstrate that the over-sampling technique greatly reduces the error. The application of MsFEM to porous media flows is considered. Finally, we describe further generalizations of MsFEM to nonlinear time-dependent equations and discuss the convergence of the method for various kinds of heterogeneities.

Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings☆

Abstract: In the present paper, several weak and strong convergence theorems are established for the three-step iterative schemes with errors for asymptotically nonexpansive mappings. Our results extend and improve the recent ones announced by Tan and Xu, Xu and Noor, and many others.

A new approach to Sobolev spaces and connections to Gamma-convergence

Abstract: This is a follow-up of a paper of Bourgain, Brezis and Mironescu [2]. We study how the existence of the limit integral(Omega)integral(Omega) omega((x)- f(y))/x - y) rho(epsilon)(x - y) dxdy as epsilon down arrow 0, (1) for omega: [0,infinity) --> [0, infinity) continuous and (rhoepsilon) subset of L-1(R-N) converging to delta(0), is related to the weak regularity of f is an element of L-loc(1)(Omega). This approach gives an alternative way of defining the Sobolev spaces W-1,W-p. We also briefly discuss the Gamma-convergence of (1) with respect to the L-1(Omega)-topology.

Discrete Laplace--Beltrami operators and their convergence

Abstract: The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for these discrete Laplace-Beltrami operators are established under various conditions. Numerical results that support the theoretical analysis are given. Application examples of the proposed discrete Laplace-Beltrami operators in surface processing and modelling are also presented.

On the Convergence of a Population-Based Global Optimization Algorithm

Abstract: In global optimization, a typical population-based stochastic search method works on a set of sample points from the feasible region. In this paper, we study a recently proposed method of this sort. The method utilizes an attraction-repulsion mechanism to move sample points toward optimality and is thus referred to as electromagnetism-like method (EM). The computational results showed that EM is robust in practice, so we further investigate the theoretical structure. After reviewing the original method, we present some necessary modifications for the convergence proof. We show that in the limit, the modified method converges to the vicinity of global optimum with probability one.

Common Lyapunov functions and gradient algorithms

Abstract: This note is concerned with the problem of finding a quadratic common Lyapunov function for a large family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families.

Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems

Abstract: We propose the use of sequences of separable, piecewise linear approximations for solving nondifferentiable stochastic optimization problems. The approximations are constructed adaptively using a combination of stochastic subgradient information and possibly sample information on the objective function itself. We prove the convergence of several versions of such methods when the objective function is separable and has integer break points, and we illustrate their behavior on numerical examples. We then demonstrate the performance on nonseparable problems that arise in the context of two-stage stochastic programming problems, and demonstrate that these techniques provide near-optimal solutions with a very fast rate of convergence compared with other solution techniques.

Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays

Abstract: First, convergence of continuous-time Bidirectional Associative Memory (BAM) neural networks are studied. By using Lyapunov functionals and some analysis technique, the delay-independent sufficient conditions are obtained for the networks to converge exponentially toward the equilibrium associated with the constant input sources. Second, discrete-time analogues of the continuous-time BAM networks are formulated and studied. It is shown that the convergence characteristics of the continuous-time systems are preserved by the discrete-time analogues without any restriction imposed on the uniform discretionary step size. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Convergence of Traffic Assignments: How Much Is Enough? 1

Abstract: Daily traffic assignments to a large-scale road network are described for Build and No-Build scenarios to evaluate the addition of two proposed ramps between I-295 and SR-42 in the New Jersey part of the Delaware Valley Region. The road network consists of 39,800 links connecting 1,510 zones. The user-equilibrium traffic assignment problem was solved with a new algorithm called origin-based assignment (OBA), which can achieve highly converged solutions with reasonable computing effort. Following a description of the user-equilibrium traffic assignment problem and the OBA algorithm, the stability of link flow differences between the two scenarios in the vicinity of the proposed ramps are examined over a broad range of assignment convergence levels. Then, link flow differences over this range of convergence levels are compared to link flow differences between two very highly converged solutions. Examination of the findings reveals in the authors' view that a relative gap of 0.01% (0.0001) is required to assure that the traffic assignments are sufficiently converged to achieve link flow stability. These convergence levels are then interpreted in terms of the number of Frank-Wolfe iterations needed to achieve comparable relative gaps, as well as the computational effort required.

Multiplication-free iterative algorithm for LS problem

Abstract: Many iterative techniques are available to solve normal equations appearing in the linear least-squares (LS) problem However, because of multiplications and divisions they cannot be effectively implemented in real time A novel multiplication-free and division-free iterative technique, the dichotomous co-ordinate descent algorithm, which guarantees convergence to the true solution under realistic assumptions, is proposed

Domain decomposition methods for the coupling of surface and groundwater flows

Abstract: The purpose of this thesis is to investigate, from both the mathematical and numerical viewpoint, the coupling of surface and porous media flows, with particular concern on environmental applications. Domain decomposition methods are applied to set up effective iterative algorithms for the numerical solution of the global problem. To this aim, we reformulate the coupled problem in terms of an interface (Steklov-Poincare) equation and we investigate the properties of the Steklov-Poincare operators in order to characterize optimal preconditioners that, at the discrete level, yield convergence in a number of iterations independent of the mesh size h. We consider a new approach to the classical Robin-Robin method and we reinterpret it as an alternating direction iterative algorithm. This allows us to characterize robust preconditioners for the linear Stokes/Darcy problem which improve the behaviour of the classical Dirichlet- Neumann and Neumann-Neumann ones. Several numerical tests are presented to assess the convergence properties of the proposed algorithms. Finally, the nonlinear Navier-Stokes/Darcy coupling is investigated and a general nonlinear domain decomposition strategy is proposed for the solution of the interface problem, extending the usual Newton or fixed-point based algorithms.

Generalized monotonically convergent algorithms for solving quantum optimal control problems

Abstract: A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

The Convergence of Contrastive Divergences

Abstract: This paper analyses the Contrastive Divergence algorithm for learning statistical parameters. We relate the algorithm to the stochastic approximation literature. This enables us to specify conditions under which the algorithm is guaranteed to converge to the optimal solution (with probability 1). This includes necessary and sufficient conditions for the solution to be unbiased.

Locally constructed algorithms for distributed computations in ad-hoc networks

Abstract: In this paper we develop algorithms for distributed computation of a broad range of estimation and detection tasks over networks with arbitrary but fixed connectivity. The distributed algorithms we develop are linear dynamical systems that generate sequences of approximations to the desired computation. The algorithms are locally constructed at each node by exploiting only locally available and macro-scopic information about the network topology. We present methods for designing these distributed algorithms so as to optimize the convergence rates to the desired computation and demonstrate their performance characteristics in the context of a problem of signal estimation from multi-node signal observations in Gaussian noise.

On the superlinear local convergence of a filter-SQP method

Abstract: Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by Fletcher, Leyffer, and Toint [8]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure. Moreover, it is shown that the modified trust-region filter-SQP method has the same global convergence properties as the original algorithm in [8].

Convergence analysis of the direct algorithm

Abstract: The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from nonsmooth analysis, and our framework is based on recent results for the MADS sampling algorithms.

Robot Convergence via Center-of-Gravity Algorithms

Abstract: Consider a group of N robots aiming to converge towards a single point. The robots cannot communicate, and their only input is obtained by visual sensors. A natural algorithm for the problem is based on requiring each robot to move towards the robots’ center of gravity. The paper proves the correctness of the center-of-gravity algorithm in the semi-synchronous model for any number of robots, and its correctness in the fully asynchronous model for two robots.