Conditions For Convergence Of Algorithm Research Articles

On Application of Fixed Point Theorem to Insurance Loss Model

The future development when an insurance company is in a difficult circumstance can be described by a stochastic process which the insurance company is tasked to manage effectively in order to achieve best goal of the company. Application of an effective risk or loss management model in an insurance company brings in more revenue for the insurer and less conditional pay-out of claims to the insured. Insurance losses, risks and premium calculation or pricing have been active and essential topics in insurance and actuarial literatures but most of these literatures did not only stand the test of time due to dynamic nature of insurance principles and practices in highly evolving environment but also lack the intuitive and detailed standard rating logic to adjust loss rating to a particular experience. There is a need to strike a balance in charging an appropriate and equitable premium by applying a suitable loss model that gives a sufficient uniquely determined solution that will not necessarily put an insurer or the insured in uncertain awkward business situations. Therefore, the objective of this research is to obtain sufficient conditions for convergence of algorithm towards a fixed point under typical insurance loss and actuarial circumstances to achieve a uniquely determined solution. At the end, a unique fixed point was determined and the algorithm formulated converges towards that point through straightforward and simplified generalised formulae and functions.

Iterative learning control for linear generalized distributed parameter system

In this paper, we use the iterative learning control algorithm to deal with generalized distributed parameter system with parabolic type which described by generalized partial differential equation. Because of the particularity of the generalized system, we usually need generalized value decomposition, but the algorithm we proposed in this paper does not need to consider the impulsive solution of the generalized system, so it can simplify the calculation process. A novel generalized theoretical result is presented by using the PD-type learning law under some assumptions. The convergence conditions of algorithm are established. By the basic generalized theory, matrix theory and mapping principle, the paper gives rigorous convergence proof of the algorithm to ensure the tracking error is convergent in L2 norm. Finally, we use an example to verify the validity of the new proposed algorithm. Through this paper, we can do further study and discuss the iterative learning algorithm for generalized distributer parameter system in the future.

Utilization of PMU Measurements for Three-Phase Line Parameter Estimation in Power Systems

A new method is developed for synchrophasor-based estimation of three-phase transmission line (TL) impedance parameters, applicable for both fully transposed and untransposed TLs. The method is based on accurate time-synchronized measurements of the voltage and current phasors at both ends of a TL. The method estimates the line impedance values using a robust estimator with the property that the influence of outliers on the final results is minimized. A robust estimator is chosen as an alternative to well-known ordinary least-squares estimators which are highly sensitive to outliers. The performance of the method has been evaluated using a laboratory setup simulating real power system conditions. The necessary conditions for algorithm convergence as well as the requirements for measurement accuracy have been studied. In addition, this paper describes validation results of the proposed method in real high-voltage power system conditions by measuring voltage and current phasors with two phasor measurement units installed on both terminals of a 400-kV fully transposed overhead TL.

Iterative Learning Control with Forgetting Factor for Linear Distributed Parameter Systems with Uncertainty

Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty coefficients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence proof of the algorithm. Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm.

A new algorithm for state estimation of stochastic linear discrete systems

A novel algorithm is proposed for state estimation of linear discrete-time systems. The procedure performs explicit minimization of the innovation variance and is based upon the principle of pseudo linear regression (PLR) method. Sufficient conditions for algorithm convergence are also derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An overall study of convergence conditions for algorithms in nonlinear programming

Since the point-to-set maps were introduced by Zangwill[1] in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established. In this paper, the relations among all these conditions are illustrated by a unified approach; still more, unlike the sufficient conditions previously given in the literature, a new necessary condition is put forward at the end of the paper, so that it implies more applications.

Computational issues in parameter estimation and feedback control problems for partial differential equation systems

We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems,(ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. Sufficient conditions for convergence of algorithms for these problems are discussed; in both cases, some type of adjoint or costate system convergence is required in addition to the expected system convergence. Examples are discussed that illustrate computational difficulties which may arise if only convergence of the approximate system holds (i.e., in the event costate convergence does not hold).

Interactive Identification and Optimization Using a Binary Preference Relation

This paper considers the problem in which a single decision maker must choose an element from a known nonempty choice set Y of multi-attributed elements when his preferences are uncertain. The preferences are uncertain in the sense that they are not explicitly available. The decision-maker's preferences are assumed to take the form of a binary relation on Y. We present an algorithm that requires the identification of preferences during the search process. The convergence of the adopted algorithm to a best element in Y relative to whatever preferences obtain is proved under the assumption that the identification of preferences is costless. We show that the sufficient conditions for convergence of this algorithm are weaker than the sufficient conditions for convergence of the interactive algorithm for the multiple criteria problem developed by Geoffrion, Dyer, and Feinberg.

On the convergence of sequential minimization algorithms

This note discusses the conditions for convergence of algorithms for finding the minimum of a function of several variables which are based on solving a sequence of one-variable minimization problems. Theorems are given which contrast the weakest conditions for convergence of gradient-related algorithms with those for more general algorithms, including those which minimize in turn along a sequence of uniformly linearly independent search directions.