Truncated Newton method for sparse unconstrained optimization using automatic differentiation

When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986.     

应用自动微分的Newton-PCG算法

一类新的使用符号微分的Newton-PCG型算法在文献[1]和[2]被导出来了。本文建立和研究应用自动微分的相应的Newton-PCG算法，理论分析和数值实验结果显示应用自动微分之后，目标函数的维数或复杂性越大，Newton-PCG算法对Newton法的改进越显著。     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.     

A Supergene Differentiation Model for Orebearing Granitic Magma

According to the features of geophysics, experimental petrology, granite geology and geochemistry, the differentiations of ore-bearing granitic magmas are discussed. It is put forward that only the supergene differentiations of ore-bearing granitic magma might exist, instead of the hypogene one of the magma. Based on it, a supergene differentiation model for the ore-bearlng granitic magma is presented.     

Asymptotic properties of an HIV/AIDS model with a time delay

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe.     

Differential algebraic equations with after-effect

In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

KNbO3：Fe晶体的时间微分效应及图像追踪

本文观察到了KNbO_3:Fe晶体的时间微分效应,并用这个微分效应进行了图像追踪的演示,为KNbO_3:Fe晶体在光折变器件领域的应用进行了有益的探索。     

Synthesis and Crystal Structure of 3,3′-(Hexane-1,6-diyl)bis(1-acetyl-5,5-dimethylhydantoin),a New Inducer of Differentiation

1 INTRODUCTION Hexamethylenebis[acetamide] (HMBA) is an effective agent in phaseⅡclinical trial[1] that induces differentiation of certain types of tumors to nonmalignant phenotypes. In an attempt to discover more efficient inducers, a number of derivatives of HMBA have been synthesized and evaluated in vitro[2, 3]. The results proved that increasing the number of functional groups could enhance the anticancer activity. In addition, it was evident that compounds with six methylene i…     

Resolution method for overlapping peaks based on the fractional-order differential

Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders. Also, equations between the differential order and the zero-crossing of the fractional-order differential of the specified peak signals are proposed according to the variation of the zero-crossing of the specified peak signals at different orders. Characteristic paramters of the Gaus- sian peak, Lorentzian peak, and Tsallis peak can be estimated using estimator I and estimator II which are obtained by the equations above. As a result, a new method is presented to resolve the overlapped peaks signal. Firstly, a fractional-order differential of the specified peak signals is obtained with the fractional-order differentiation filter. Then, characteristic paramters of the specified peak signals can be extracted using estimator I and estimator II. Finally, the Tsallis peak is used as a model to assign the overlapping peak signals correctly. Experimental results show that the proposed method is efficient and effective for the simulated overlapping peaks and detected overlapping voltammetric peak signals.