Showing papers on "Convergence (routing) published in 1975"
TL;DR: In this paper, a stepsize procedure is proposed to maintain monotone decrease of an exact penalty function, and the convergence of the damped Newton method is globalized in unconstrained optimization.
Abstract: Recently developd Newton and quasi-Newton methods for nonlinear programming possess only local convergence properties. Adopting the concept of the damped Newton method in unconstrained optimization, we propose a stepsize procedure to maintain monotone decrease of an exact penalty function. In so doing, the convergence of the method is globalized. Keywords: nonlinear programming, global convergence, exact penalty function.
1,077 citations
TL;DR: In this paper, the convergence of interpolating sequences of rational functions with partly free poles is studied and the authors consider the problem of finding the minimum number of free poles for a rational function.
Abstract: The paper considers questions of the convergence of interpolating sequences of rational functions with partly free poles.Bibliography: 16 titles.
126 citations
Abstract: The problem of convergence of Pade approximants for some classes of meromorphic functions is considered in this paper.Bibliography: 13 titles.
118 citations
TL;DR: In this paper, a cutting plane algorithm for the solution of generalized geometric programs with bounded variables is described and illustrated by the detailed solution of a small numerical example, and convergence of this algorithm to a Kuhn-Tucker point of the program is assured if an initial feasible solution is available to initiate the algorithm.
Abstract: A cutting plane algorithm for the solution of generalized geometric programs with bounded variables is described and then illustrated by the detailed solution of a small numerical example. Convergence of this algorithm to a Kuhn-Tucker point of the program is assured if an initial feasible solution is available to initiate the algorithm. An algorithm for determining a feasible solution to a set of generalized posynomial inequalities which may be used to find a global minimum to the program as well as test for consistency of the constraint set, is also presented. Finally an application in optimal engineering design with seven variables and fourteen nonlinear inequality constraints is formulated and solved.
110 citations
TL;DR: Two algorithms are presented for finding a zero of a real continuous function defined on a given interval using mixtures of linear interpolation, rational interpolations, and bisectmn.
96 citations
TL;DR: A recursive algorithm for parametric identification of discrete-time systems known as Panuska's method, the approximate maximum likelihood method or the extended matrix method is analyzed and the manner in which the counterexamples are constructed yields insight into the algorithm and provides ideas to improve the convergence properties.
Abstract: A recursive algorithm for parametric identification of discrete-time systems known as Panuska's method, the approximate maximum likelihood method or the extended matrix method, is analyzed. Making use of recently developed theory for asymptotic analysis of recursive stochastic algorithms, dynamic systems, and autoregressive moving average (ARMA) processes are constructed for which this algorithm does not converge. The manner in which the counterexamples are constructed yields insight into the algorithm and provides ideas how to improve the convergence properties.
85 citations
TL;DR: In this article, the convergence of some rearrangements of series in the Walsh-Paley system was studied and it was shown that the Walsh and Walsh-Kaczmarz systems are convergence systems.
Abstract: In the paper one considers the convergence of some rearrangements of series in the Walsh-Paley system. In particular, one shows that the Walsh and Walsh-Kaczmarz systems are convergence systems.
81 citations
TL;DR: In this paper, an extension of the dominant eigenvalue method is presented and its effectiveness is tested with simulations of chemical processes and the method is compared to previously available methods and is found to achieve convergence more rapidly and indeed was effective in cases where some other methods were ineffective or did not take a promotion step at all.
Abstract: The objective of this study was to devise an improved method of accelerating the iterative computation of steady state simulations of chemical processes. An extension of the dominant eigenvalue method is presented and its effectiveness is tested with simulations of chemical processes. The method is compared to previously available methods and is found to achieve convergence more rapidly and indeed was effective in cases where some other methods were ineffective or did not take a promotion step at all. The proposed method is applicable to the acceleration of any iterative computation of a nonlinear fixed-point problem.
67 citations
55 citations
TL;DR: This paper presents a globally convergent multiplier method which utilizes an explicit formula for the multiplier, which automatically calculates a value for the penalty coefficient, which, under certain assumptions, leads to global convergence.
Abstract: This paper presents a globally convergent multiplier method which utilizes an explicit formula for the multiplier. The algorithm solves finite dimensional optimization problems with equality constraints. A unique feature of the algorithm is that it automatically calculates a value for the penalty coefficient, which, under certain assumptions, leads to global convergence.
01 Jan 1975
TL;DR: In this paper, a nonconforming finite element, Wilson's element, for solving the elastic problem is mathematically studied and the errors on the stresses and displacements are shown to be asymptotically of order h and h 2, respectively, where h is the supremum of the lengths of the sides of the elements.
Abstract: Abstract A nonconforming finite element, Wilson's element, for solving the elastic problem is mathematically studied. This element passes the patch-test. The errors on the stresses and displacements are shown to be asymptotically of order h and h 2 , respectively, where h is the supremum of the lengths of the sides of the elements.
TL;DR: In this article, a method has been developed for selection of the set of torn streams in a process simulation that leads to convergence of a direct substitution calculation in the minimum number of iterations.
Abstract: A method has been developed for selection of the set of torn streams in a process simulation that leads to convergence of a direct substitution calculation in the minimum number of iterations. It is based on the establishment of families of decompositions, the members of each of which have identical convergence behavior. Explicit criteria for choice among families have been found that lead, in almost every case, to a single optimum decomposition family. These results have been verified by application to several chemical process simulation examples.
TL;DR: In this article, conditions for the weak convergence of weighted empirical cumulative processes of three types of mixing random variables (rv's) were given for the convergence of a weighted cumulative process of a mixing random variable.
Abstract: Conditions are given for the weak convergence of weighted empirical cumulative processes of three types of mixing random variables (rv's) on $\lbrack 0, 1\rbrack$.
TL;DR: In this paper, it was shown that a quadrature rule for Cauchy principal value integrals converges for functions satisfying a Holder condition of order one, and this result was extended to demonstrate convergence of the rule for Holder continuous functions of any order greater than zero.
Abstract: In a previous paper the authors proved that a quadrature rule for Cauchy principal value integrals converged for functions satisfying a Holder condition of order one. This result is now extended to demonstrate convergence of the rule for Holder continuous functions of any order greater than zero.
TL;DR: In this article, a new density matrix algorism is proposed for the Hartree-Fock calculation in the restricted basis approximation, which is shown to have a satisfactory behavior in convergence.
Abstract: A new density matrix algorism is proposed for the Hartree-Fock calculation in the restricted basis approximation The algorism is shown to have a satisfactory- behavior in convergence It is 11lso capable of obtaining high energy solutions- of the Hartree-F ock equation A CND0/2 computer ·program for the closed shell case making use of the _new algorism is tested mainly for carbon mono-oxide Its computational speed is comparable to that of the usual method at the equilibrium nuclear configuration It becomes faster than the usual one as the interatomic distance increases and converges with a nearly constant speed even at nuclear configurations where the usual one does not converge The structure of the Hartree-Fock energy surface in the variation space is illustrated for the carbon mono oxide with various interatomic distances ·The origin of the troubles in convergence is dis cussed in connection with the structure of the surface The Hartree-Fock solutions corre: sponding to the extrema of the surface are calculated and some of them are shqwn to represent the zwitter-ionic state~ of the molecule
TL;DR: An algorithm for the time domain approximation of discrete systems with a recursion is described, which achieves better results than the currently used two-dimensional filter synthesis techniques since the starting point of the iteration is the solution of the latter approach.
Abstract: An algorithm for the time domain approximation of discrete systems with a recursion is described. The algorithm iterates towards a solution minimizing the sum of squared differences between the desired and the actual output. Convergence is guaranteed. The scheme is applied to the design of low-pass filters by time domain approximation. The results compare well with other design strategies. We have extended the algorithm to two dimensions. This algorithm is essentially the same iterative scheme used for the one-dimensional case. The two-dimensional iteration achieves better results than the currently used two-dimensional filter synthesis techniques since the starting point of the iteration is the solution of the latter approach. Usually, a few iterations suffice to improve the solution in a satisfactory amount. Convergence is also guaranteed. An example of two-dimensional impulse response approximation is also given as an illustration.
TL;DR: In this article, the authors show that the special form of the differential equation can be used to derive single and multistep methods which give improved rates of local convergence to a root.
Abstract: Methods which make use of the differential equation ẋ(t) = −J(x)−1f(x), where J(x) is the Jacobian of f(x), have recently been proposed for solving the system of nonlinear equations f(x) = 0. These methods are important because of their improved convergence characteristics. Under general conditions the solution trajectory of the differential equation converges to a root of f and the problem becomes one of solving a differential equation. In this paper we note that the special form of the differential equation can be used to derive single and multistep methods which give improved rates of local convergence to a root.
TL;DR: Two general nonlinear optimization algorithms generating a sequence of feasible solutions based on the concept of point-to-set mapping continuity are described and the results unify these apparently diverse approaches.
Abstract: Two general nonlinear optimization algorithms generating a sequence of feasible solutions are described. The justifications for their convergence are based on the concept of point-to-set mapping continuity. These two algorithms cover many conventional feasible solution methods. The convergence results unify these apparently diverse approaches.
TL;DR: In this article, the storage coefficient, a constant, and transmissivities, functions of the space variable are chosen for identification in a partial differential equation associated with an inhomogeneous aquifer system.
Abstract: This paper develops a new algorithm for parameter identification in a partial differential equation associated with an inhomogeneous aquifer system. The parameters chosen for identification are the storage coefficient, a constant, and transmissivities, functions of the space variable. An implicit finite-difference scheme is used to approximate the solutions of the governing equation. A least-squares criterion is then established. Using distributed observations on the dependent variable within the system, parameters are identified directly by solving a sequence of quadratic programming problems such that the final solution converges to the original problem. The advantages of this new algorithm include rapid rate of convergence, ability to handle any inequality constraints, andeasy computer implementation. The numerical example presented demonstrates the simultaneous identification of 12 parameters in only seconds of computer time.
IBM1
TL;DR: Application of direct iterations, based on convergent splittings, to the eigenvalue problem of large sparse symmetric matrices is discussed, and a general convergence proof is given.
08 Sep 1975
TL;DR: A general formulation of the method of multipliers is presented and a theorem characterising convergence of this method in case of linear-quadratic problems in Hilbert space is presented.
Abstract: In the paper a definition is given of a class of generalized Lagrangians, and some simple properties of them are discussed, especially those related to the topology in the set of constraints. A general formulation of the method of multipliers is presented and a theorem characterising convergence of this method in case of linear-quadratic problems in Hilbert space. Numerical examples of computing the optimal control of time lag systems to terminal functions are presented. The results indicate that the effectiveness of the method of multipliers depends on the choice of the norm in the set of constraints.
TL;DR: The application of spatial discretization (discrete ordinate method) to a class of integro-differential equations is discussed in this paper, where it is shown that consistency in the approximation of the operators implies convergence of the approximate solution to the true solution.
Abstract: The application of spatial discretization (discrete ordinate method) to a class of integro-differential equations is discussed. It is shown that consistency in the approximation of the operators implies convergence of the approximate solution to the true solution.
TL;DR: In this article, generalization of the method of Lympunov functions is outlined, whereby the convergence of numerical methods of optimization may be proved, and theorems on sufficient conditions on convergence of continuous and discrete schemes are stated and proved.
Abstract: GENERALIZATIONS of the method of Lympunov functions are outlined, whereby the convergence of numerical methods of optimization may be proved. Theorems on sufficient conditions for the convergence of continuous and discrete schemes are stated and proved. The application of the theorems is illustrated by examples.
TL;DR: In this article, it was shown that Church's theorem on convergence of the varying environments process admits of an elementary proof in this particular case, and examples were given on the asymptotic behavior of extinction probabilities in the supercritical case and conditional expectation given non-extinction in the subcritical case.
Abstract: The class of fractional linear generating functions is used to illustrate various aspects of the theory of branching processes in varying and random environments. In particular, it is shown that Church's theorem on convergence of the varying environments process admits of an elementary proof in this particular case. For random environments, examples are given on the asymptotic behavior of extinction probabilities in the supercritical case and conditional expectation given non-extinction in the subcritical case.