Showing papers on "Convergence (routing) published in 1976"
01 Jan 1976
304 citations
TL;DR: A global convergence theory for a broad class of ''monotonic'' nonlinear programming algorithms is given and actual convergence of the entire sequence of iterates and point-of-attraction theorems are established under weak hypotheses.
124 citations
Book•
01 Jan 1976
87 citations
TL;DR: A class of combined primal–dual and penalty methods for constrained minimization which generalizes the method of multipliers is proposed and analyzed and it is shown that the rate of convergence may be linear or superlinear with arbitrary Q-order of convergence depending on the problem at hand.
Abstract: In this paper we propose and analyze a class of combined primal–dual and penalty methods for constrained minimization which generalizes the method of multipliers. We provide a convergence and rate of convergence analysis for these methods for the case of a convex programming problem. We prove global convergence in the presence of both exact and inexact unconstrained minimization, and we show that the rate of convergence may be linear or superlinear with arbitrary Q-order of convergence depending on the problem at hand and the form of the penalty function employed.
79 citations
TL;DR: In this article, the convergence rates for the error between the solution to a discrete approximation of a fixed time, unconstrained control problem and the corresponding continuous optimal control were derived for one-step and multistep integration schemes.
Abstract: Convergence rates for the error between the solution to a discrete approximation of a fixed time, unconstrained control problem and the corresponding continuous optimal control are derived for one-step and multistep integration schemes The convergence rate for multistep schemes depends on the order of the integration scheme and the approximation properties of the discrete costate equation at the right endpoint Furthermore, the order is $ \leqq 3$ and the error in the optimal discrete control exhibits a boundary layer with most of the error concentrated at the right endpoint For a class of one-step integration schemes satisfying a symmetry condition, second order convergence of the optimal discrete control is both proved and observed experimentally The computations also indicate that the convergence rate of the optimal discrete state and costate variables equals the order of the integration scheme By an auxiliary computation, this order can also be recovered for the control approximation Some numeric
69 citations
TL;DR: A new two level method is developed for the optimization of non-linear dynamical systems with a quadratic cost function that takes less than half the computation time of the global solution.
49 citations
TL;DR: In this paper, the convergence properties of iterative orthogonalization processes are investigated using polar decomposition of matrices, and the convergence rate and the range of convergence is established in terms of the spectral radius of the modulus of the matrix which is being orthogonalyzed.
Abstract: Polar decomposition of matrices is used here to investigate the convergence properties of iterative orthogonalization processes. It is shown that, applying this decomposition, the investigation of a general iterative process of a certain form can be reduced to the investigation of a scalar iterative process which is simple. Three known iterative orthogonalization processes, which are special cases of the general process, are analyzed, their convergence rate (order) is determined, and their range of convergence is established in terms of the spectral radius of the modulus of the matrix which is being orthogonalyzed.
42 citations
TL;DR: In this article, the authors present a method of synthesizing time-histories from a given design response spectrum, which can be described as floor responses at a particular location in a plant, or they may be descriptive of seismic ground motions at a plant site.
41 citations
TL;DR: In this article, the authors proposed a method to identify the closed-loop parameters of a linear dynamical system with a time delay based on the equation error, which is based on composite delayed state variables.
Abstract: The subject of this short paper is on-line identification of the parameter vector defining a linear dynamical system which operates in a closed loop in the presence of noise, and incorporates a time delay. The method is based on the equation error. Other known subsystems in the closed-loop system increase the dimension of the closed-loop parameter vector which tends to degrade the estimation convergence process. By means of "composite state variables," introduced in this short paper, this increase is prevented and the open-loop parameters are directly identified from closed-loop input-output data. The pure time delay in the closed loop causes a representation problem in the equation error formulation. This is overcome by "composite delayed state variables." The value of the time delay is determined by means of excess parameters provided by a "higher order model" and a simple on-line search procedure. The method is illustrated by simulated examples.
TL;DR: In this paper, the authors present a framework for the study of the convergence properties of optimal control algorithms and illustrate its use by means of two examples. The framework consists of an algorithm prototype with a convergence theorem, together with some results in relaxed controls theory.
Abstract: This paper presents a framework for the study of the convergencee properties of optimal control algorithms and illustrates its use by means of two examples. The framework consists of an algorithm prototype with a convergence theorem, together with some results in relaxed controls theory.
01 Jan 1976
TL;DR: In this article, a criterion for L 1-convergence of a certain cosine sum with quasi semi-convex coecients is obtained, and a necessary and sucient condition for the cosine series is deduced as a corollary.
Abstract: In this paper a criterion for L1- convergence of a certain cosine sums with quasi semi-convex coecients is obtained. Also a necessary and sucient condition for L1-convergence of the cosine series is deduced as a corollary.
01 Jan 1976
TL;DR: In this paper, a computational method for carrying out MC SCF calculations using as basis configuration the bonded functions of Boys et al. is described, and the method described here utilizes many of the techniques used in such calculations, particularly the use of a list symbolic matrix elements.
TL;DR: In this paper, one-dimensional numerical analysis of complete semiconductor device equations is applied to the p-n-p-n four layer structure with an arbitrary impurity doping profile and arbitrary carrier lifetimes, to calculate the thyristor DC forward voltages and the holding current.
Abstract: One-dimensional numerical analysis of complete semiconductor device equations is applied to the p-n-p-n four layer structure with an arbitrary impurity doping profile and arbitrary carrier lifetimes, to calculate the thyristor DC forward voltages and the holding current. In the beginning, a numerical method of the current-control type is presented, with discussion about the convergence of the iterative process involved. Then a set of standard numerical values is given to the parameters to describe the impurity doping condition. Computation results are demonstrated for a variety of carrier lifetimes and current densities. Endeavor will be made to understand basic device physics through the computed carrier densities, electric fields, potentials and currents. The computation results also include the static current vs voltage characteristics, which are immediately concerned with the actual design and fabrication of thyristors. Specifically for the design of high speed thyristors, a preferable condition is provided by keeping lifetimes in the shorter base to a high value and those in the longer base to a low value.
TL;DR: Three computational methods which extend to nonlinearly constrained minimization problems the efficient convergence properties of, respectively, the method of steepest descent, the variable metric method, and Newton’s method for unconstrained minimization are presented.
Abstract: This paper presents three computational methods which extend to nonlinearly constrained minimization problems the efficient convergence properties of, respectively, the method of steepest descent, the variable metric method, and Newton’s method for unconstrained minimization. Development of the algorithms is based on use of the implicit function theorem to essentially convert the original constrained problem to an unconstrained one. This approach leads to practical and efficient algorithms in the framework of Abadie’s generalized reduced gradient method. To achieve efficiency, it is shown that it is necessary to construct a sequence of approximations to the Lagrange multipliers of the problem simultaneously with the approximations to the solution itself. In particular, the step size of each iteration must be determined by a linesearch for a minimum of an approximate Lagrangian function.
TL;DR: A test for nonoptimal actions in undiscounted Markov decision chains is proposed, which eliminates actions for one or more stages after which they may re-enter the set of possibly optimal actions, but as convergence proceeds such re-entries cease.
Abstract: A test for nonoptimal actions in undiscounted Markov decision chains is proposed. The test eliminates actions for one or more stages after which they may re-enter the set of possibly optimal actions, but as convergence proceeds such re-entries cease.
01 Jan 1976
TL;DR: A lower semicontinuity theorem for integral functionals is proved under LI-strong convergence of trajectories and Lrweak convergence of the control functions in this paper, and an alternative statement is also proved under pointwise convergence of trajectory trajectories.
Abstract: A lower semicontinuity theorem for integral functionals is proved under LI-strong convergence of the trajectories and Lrweak convergence of the control functions. An alternative statement is also proved under pointwise convergence of the trajectories.
TL;DR: In this paper, the Hermite expansion from a least square standpoint is used for the inference of the probability distribution in the absence of excluded volume effects for the first 10 moments of the R2p vector.
Abstract: Methods are presented for facilitating the calculation of even moments 〈R2p〉 of the end to end vector R and for the inference of the probability distribution in the absence of excluded volume effects. The gain in efficiency of moment calculations is several hundredfold for the first 10 moments, 0⩽p⩽10. The proposed inference scheme is similar to the Hermite expansion from a least square standpoint but differs in choice of weight function. Tests on freely rotating chains exhibit quantitatively useful convergence for all R, including chains with too few bonds to permit ring closure.
TL;DR: In this article, the convergence of a finite element approximation for a variational inequality related to hydraulics is studied and error bounds in terms of the mesh size and a theorem of convergence of the domains are derived.
Abstract: In this paper we study the convergence of a finite element approximation for a variational inequality related to hydraulics and we prove, for both linear and quadratic elements, error bounds in terms of the mesh size and a theorem of convergence of the domains
TL;DR: In this paper, the convergence of nets of probability measures on a topological group was studied and a new technique for studying the convergence was developed for analyzing the interplay between convergence and convolutions of measures like properties of convolution mapping, divisibility of measures and convolution semigroups.
Abstract: A new technique is developed for studying the convergence of nets of probability measures on a topological group. It is applied to results concerned with the interplay between convergence and convolutions of measures like properties of the convolution mapping, divisibility of measures and convolution semigroups. Our method gives a unified and simple approach to these results.
TL;DR: In this paper, a variational principle is derived from the spectral theorem of self-adjoint operators, which allows to calculate simultaneously upper and lower bounds for each point of the spectrum, and the convergence of this method and the equivalence with the nonlinear problem of variation are proven.
Abstract: A variational principle is derived from the spectral theorem of self-adjoint operators. The principle allows to calculate simultaneously upper and lower bounds for each point of the spectrum. For Schrodinger operators this method of error minimization is reduced to a series of matrix diagonalizations using an iterative process and is linearized in this way. The convergence of this method and the equivalence with the nonlinear problem of variation are proven.
TL;DR: In this paper, the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared.
Abstract: In this note the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared. The vehicle for the comparison is a twelth-order complex counter-current example taken from the literature. The computational load for the two methods is compared qualitatively whereas the convergence characteristics arc tested on the example. A simple condition is also given for the convergence of the interaction prediction method. This is also tested on the example.
TL;DR: In this article, the convergence of rational approximations in infinite sectors symmetric about the positive real axis was studied, and it was shown that the convergence rate of rational approximation is bounded.
Abstract: In this paper, we study the geometric convergence of rational approximations toe ?z in infinite sectors symmetric about the positive real axis.
01 Dec 1976
TL;DR: An improved adaptive observer is formulated for nth order, linear, single-output, observable and time invariant systems and uses only input and output measurements and has an arbitrarily fast rate of convergence for both the system state and the system parameters.
Abstract: Based on the implementation and the method of approach, the adaptive observers are herein classified as explicit and implicit observers. Both types are discussed from a convergence point of view, and a geometrical interpretation of the adaptive algorithms is given in order to account for their slow rate of convergence. Finally, an improved adaptive observer is formulated for nth order, linear, single-output, observable and time invariant systems. The proposed scheme uses only input and output measurements, is globally asymptotically stable and has an arbitrarily fast rate of convergence for both the system state and the system parameters. Simulation results are included.