Showing papers on "Convergence (routing) published in 1982"
TL;DR: The important new feature of the proposed algorithms is their ability to ignore redundant data and the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm.
725 citations
01 Jan 1982
TL;DR: The watchdog technique is described and discussed, and some global and Q-superlinear convergence properties are proved.
Abstract: The watchdog technique is an extension to iterative optimization algorithms that use line searches. The purpose is to allow some iterations to choose step-lengths that are much longer than those that would be allowed normally by the line search objective function. Reasons for using the technique are that it can give large gains in efficiency when a sequence of steps has to follow a curved constraint boundary, and it provides some highly useful algorithms with a Q-superlinear rate of convergence. The watchdog technique is described and discussed, and some global and Q-superlinear convergence properties are proved.
301 citations
TL;DR: In this article, the authors prove that a predetermined sequence of step sizes (in a descent direction) would guarantee, under certain regularity conditions, convergence to the equilibrium solution under a given regularity condition.
Abstract: The focus of this paper is on a certain class of equilibrium traffic assignment problems characterized by a path formulation of the associated mathematical programs. In such cases the equilibration iterations would require path enumeration, and are therefore prohibitively expensive. In this paper we prove that a predetermined sequence of step sizes (in a descent direction) would guarantee, under certain regularity conditions, convergence to the equilibrium solution. This algorithm was suggested in the literature without a proof of convergence, which we give here.
279 citations
TL;DR: The convergence rate of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased as mentioned in this paper, and the convergence rate depends on the strategy used to increase the degree of freedom.
Abstract: The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative strategies are examined in the light of recent theoretical results and computational experience.
194 citations
TL;DR: In this paper, a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design is proposed for a large class of parabolic distributed systems, where the observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation.
Abstract: A compensator design is proposed for a large class of parabolic distributed systems. Basically, it is a modal approach utilizing known finite-dimensional algorithms for observer and stabilizer design. The observer is constructed from observations taken from point or averaging sensors and the compensator is a feedback of this observer and can be a "distributed" or "boundary" implementation. Explicit sufficient conditions are given for the convergence of this scheme.
163 citations
TL;DR: In this paper, the authors consider the application of a general class of quasi-Newton methods to the solution of the classical equality constrained nonlinear optimization problem and develop necessary and sufficient conditions for the Q-superlinear convergence of such methods and present a companion linear convergence theorem.
Abstract: We consider the application of a general class of quasi-Newton methods to the solution of the classical equality constrained nonlinear optimization problem. Specifically, we develop necessary and sufficient conditions for the Q-superlinear convergence of such methods and present a companion linear convergence theorem. The essential conditions relate to the manner in which the Hessian of the Lagrangian function is approximated.
156 citations
TL;DR: In this article, a method of estimating the rate of convergence of approximation to convex, control-constrained optimal control problems is proposed, where conditions of optimality involving projections on the set of admissible control are exploited.
Abstract: A method of estimating the rate of convergence of approximation to convex, control-constrained optimal-control problems is proposed. In the method, conditions of optimality involving projections on the set of admissible control are exploited. General results are illustrated by examples of Galerkin-type approximations to optimal-control problems for parabolic systems.
154 citations
TL;DR: The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared in this article, where the convergence properties are derived from corresponding approximate energy expressions.
Abstract: The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared All of the iterative methods considered here are derived from corresponding approximate energy expressions These energy expressions are discussed within the context of their suitability for the calculation of noninfinitesimal wave function corrections A method based on the partitioned orbital Hessian matrix and which uses an approximate super‐CI secular equation for the wave function corrections is shown to posses second‐order convergence and to have the largest radius of convergence of the methods analyzed in detail in this work for several molecular examples Particular attention is given to convergence properties for excited states, where the differences between these methods are most significant
150 citations
TL;DR: It is shown that minimum queuing delay path algorithms tend to exhibit violent oscillatory behavior in the absence of a damping mechanism, and two types of schemes are analyzed in this paper.
Abstract: Several proposed routing algorithms for store and forward communication networks, including one currently in operation in the ARPANET route messages along shortest paths computed by using some set of link lengths. When these lengths depend on current traffic conditions as they must in an adaptive algorithm, dynamic behavior questions such as stability, convergence, and speed of convergence are of interest. This paper is the first attempt to analyze systematically these issues. It is shown that minimum queuing delay path algorithms tend to exhibit violent oscillatory behavior in the absence of a damping mechanism. The oscillations can be damped by means of several types of schemes two of which are analyzed in this paper. In the first scheme a constant bias is added to the queuing delay thereby providing a preference towards paths with a small number of links. In the second scheme the effects of several past routings are averaged as for example when the link lengths are computed and communicated asynchronously throughout the network.
128 citations
TL;DR: The convergence of two relaxation algorithms designed to solve, respectively, the extended single-mode and the general multimodal network equilibrium problems are established.
Abstract: In this paper we establish the convergence of two relaxation algorithms designed to solve, respectively, the extended single-mode and the general multimodal network equilibrium problems. Both algorithms are shown to converge linearly; the first under the assumption that the cost functions are not too asymmetric; the second under the assumption that the cost interaction among the different modes is relatively weak.
128 citations
Journal Article•
TL;DR: In this article, sufficient conditions for the convergence of a certain class of algorithms (diagonalization algorithms) for equilibrium traffic assignment problems with link user cost functions that may depend on the flows of several modes on all the links of the network and have asymmetric Jacobian matrices are provided.
Abstract: The purpose of this paper is to provide sufficient conditions for the convergence of a certain class of algorithms (diagonalization algorithms) for equilibrium traffic assignment problems with link user cost functions that may depend on the flows of several modes on all the links of the network and have asymmetric Jacobian matrices. These problems do not have equivalent convex cost minimization formulations and may not be solved with the adaptation of a suitable nonlinear programming method. (TRRL)
TL;DR: In this article, a scheme is devised which drastically reduces the number of iterations required to reach self-consistency in electronic-structure calculations, particularly helpful in calculations for systems with large unit cells.
Abstract: A scheme is devised which drastically reduces the number of iterations required to reach self-consistency in electronic-structure calculations. This scheme is particularly helpful in calculations for systems with large unit cells.
TL;DR: Romberg's method gives fast convergence to an answer containing more significant digits than usual methods provide and is applied to improve the accuracy in the computation of the first and second derivatives of a real function.
TL;DR: Global convergence of the algorithm is proven under very weak assumptions and the proof relates this technique to other iterative methods that have been suggested for general linear programs.
Abstract: An iterative aggregation procedure is described for solving large scale, finite state, finite action Markov decision processes MDPs. At each iteration, an aggregate master problem and a sequence of smaller subproblems are solved. The weights used to form the aggregate master problem are based on the estimates from the previous iteration. Each subproblem is a finite state, finite action MDP with a reduced state space and unequal row sums. Global convergence of the algorithm is proven under very weak assumptions. The proof relates this technique to other iterative methods that have been suggested for general linear programs.
Journal Article•
TL;DR: It is proved that pattern recognition procedures derived from orthogonal series estimates of a probability density function are Bayes risk consistent and do not lose their asymptotic properties even if the random environment is nonstationary.
Abstract: Van Ryzin and Greblicki showed that pattern recognition procedures derived from orthogonal series estimates of a probability density function are Bayes risk consistent. In this note it is proved that these procedures do not lose-under some additional conditions-their asymptotic properties even if the random environment is nonstationary.
TL;DR: A multi phase self-adaptive predictor corrector type algorithm to enable the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as potential pre/postbuckling behavior is developed.
TL;DR: A formal approach for the optimization of the final design of reload cores has been devised and verified, and led to a reduction in nodal peaks of 1 to 3% over the final designer-obtained loading pattern within a couple of iterations.
Abstract: A formal approach for the optimization of the final design of reload cores has been devised and verified. The method is based on applying the calculus of variations (Pontryagin's principle) to the normal flux and depletion system equations. The resulting set of coupled system, Euler-Lagrange (E-L), and optimality equations are solved iteratively. This is done by assuming a loading pattern for the old fuel, first solving the system equations, and then the E-L equations. The pattern is then modified by using the optimality (or Pontryagin) condition, and the process is repeated until no further improvements can be made. A computer program, OPMUV, implementing these procedures has been written and verified. The code can handle two-dimensional, quarter-core symmetric configurations with up to 241 assemblies and 4 nodes per assembly with modified one-group theory. It also has the capability of optimizing over the entire depletion cycle as well as just at the beginning of cycle (BOC). The results show that the procedure does work. In all cases tried, the method led to a reduction in nodal peaks of 1 to 3% over the final designer-obtained loading pattern within a couple of iterations. These savings carry over to comparable reductions in pin peaksmore » when the optimized patterns are used in four-group, fine-mesh calculations. Since the changes on each iteration are limited to ensure convergence, the method is thus well suited for the final fine tuning of the normally obtained patterns to gain an extra few percent in power flattening.« less
TL;DR: In this paper, a man-machine interactive algorithm for solving multiobjective optimization problems involving one decision maker is presented, and the convergence of the iterative algorithm is proved under natural assumptions on the convergence and stability of the basic Frank-Wolfe algorithm.
Abstract: A man-machine interactive algorithm is given for solving multiobjective optimization problems involving one decision maker. The algorithm, a modification of the Frank-Wolfe steepest ascent method, gives at each iteration a significant freedom and ease for the decision-maker's self-expression, and requires a minimal information on his local estimate of the steepest-ascent direction. The convergence of the iterative algorithm is proved under natural assumptions on the convergence and stability of the basic Frank-Wolfe algorithm.
01 Jan 1982
TL;DR: When finite element methods are used to solve the statwnary Stokes problem, there is a compatibility condition between the subspaces used to approximate the velocity u and the pressure p which must be satisfied to obtain optimal rates of convergence as mentioned in this paper.
Abstract: When finite element methods are used to solve the statwnary Stokes problem there is a compatibüity condition between the subspaces used to approximate'lhe velocity u and the pressure p which must be satisfied to obtain optimal rates of convergence Finite element subspaces ofarbitrary degree are constructed which have optimal rates of convergence for the statwnary Stokes problem These results include régions with curved boundanes where éléments similar to isoparametnc éléments are used Resumé — Lorsqu'on utilise des méthodes d'éléments finis pour résoudre le problème de Stokes stationnaire, les sous-espaces utilisés pour l'approximation de la vitesse u et de la pression p doivent satisfaire une condition de compatibilité afin d'obtenir des taux optimaux de convergence On construit ici des espaces d'éléments finis de degré arbitraire qui conduisent à des taux optimaux de convergence pour le problème de Stokes stationnaire Ces résultats s'appliquent en particulier à des régions à frontière courbe, où Ton utilise des éléments finis analogues aux éléments finis isoparamétriques
TL;DR: A proof of convergence is given in this paper of the T‐matrix numerical scheme, which is widely used in practice and has proved convergence of this scheme.
Abstract: The T‐matrix numerical scheme is widely used in practice. Convergence of this scheme was not proved. A proof of convergence is given in this paper.
01 Jan 1982
TL;DR: In this article, the authors review and extend results on the local convergence of the classical Newton-Kantorovich method and discuss globally convergent damped and inexact Newton methods and point out advantages of using a minimal error conjugate gradient method for the linear systems arising at each Newton step.
Abstract: We review and extend results on the local convergence of the classical Newton-Kantorovich method. Then we discuss globally convergent damped and inexact Newton methods and point out advantages of using a minimal error conjugate gradient method for the linear systems arising at each Newton step.
TL;DR: In this article, the authors present a cutting-plane algorithm for nonlinear programming which, under suitable conditions, exhibits a linear or geometric global rate of convergence, which is no better than arithmetic for problems not satisfying a Haar condition.
Abstract: This paper presents a cutting-plane algorithm for nonlinear programming which, under suitable conditions, exhibits a linear or geometric global rate of convergence. Other known rates of convergence for cutting-plane algorithms are no better than arithmetic for problems not satisfying a Haar condition. The feature responsible for this improved rate of convergence is the addition at each iteration of a new cut for each constraint, rather than adding only one new cut corresponding to the most violated constraint as is typically the case. Certain cuts can be dropped at each iteration, and there is a uniform upper bound on the number of old cuts retained. Geometric convergence is maintained if the subproblems at each iteration are approximated, rather than solved exactly, so the algorithm is implementable. The algorithm is flexible with respect to the point used to generate new cuts.
TL;DR: An algorithm for solving a minimax problem over a polyhedral set defined in terms of a system of linear inequalities that resembles that of Han, but differs from it both in the direction-finding and the line search steps.