In many engineering applications, it is often the case that observations are only available in interval form. this note, by using expectation-maximization (EM) algorithm, parameter estimation of Weibull distribution with interval-censored data considered. The estimates obtained EM algorithm compared those conventional Newton-type methods, including Davidon–Fletcher–Powell (DFP) and Berndt–Hall–...

Solar-terrestrial interactions produce a rich variety of optical emissions in the Earth’s upper atmosphere (100–1000 km). While ground based brightness measurements (i.e., column integrated photon density) provide an important diagnostic of these processes, the more interesting physics is in the associated volume emission rate distribution (i.e., photon production/cm s versus altitude). This wo...

The Barzilai–Borwein (BB) gradient method is favourable over the classical steepest descent method both in theory and in real computations. This method takes a 'fixed' step size rather than following a set of line search rules to ensure convergence. Along this line, we present a new approach for the two-point approximation to the quasi-Newton equation within the BB framework on the basis of a w...

<p style='text-indent:20px;'>Memoryless quasi–Newton updating formulas of BFGS (Broyden–Fletcher–Goldfarb–Shanno) and DFP (Davidon–Fletcher–Powell) are scaled using well-structured diagonal matrices. In the scaling approach, elements as well eigenvalues memoryless play significant roles. Convergence analysis given diagonally methods is discussed. At last, performance numerically tested on...

In a recent paper, the authors have proved results characterizing convexity-preserving maps deened on a subset of a not-necessarily nite dimensional real vector space as projective maps. The purpose of this note is threefold. First, we state a theorem characterizing continuous, injective, convexity-preserving maps from a relatively open, connected subset of an aane subspace of R m into R n as p...

In application to general function, each of the conjugate gradient and Quasi-Newton methods has particular advantages disadvantages. Conjugate (CG) techniques are a class unconstrained optimization algorithms with strong local global convergence qualities minimal memory needs. reliable efficient on wide range problems they converge faster than method require fewer function evaluations but have di...

The solubility of CO2 in the primary, secondary, tertiary and sterically hindered amine aqueous solutions at various conditions was studied. In the present work, the Modified Kent-Eisenberg (M-KE), the Extended Debye-Hückel (E-DH) and the Pitzer models were employed to study the solubility of CO2 in amine aqueous solutions. Two explicit equations are presented to evalu...

A new rank-two variable-metric method is derived using Greenstadt's variational approach [Math. Comp., this issue]. Like the Davidon-Fletcher-Powell (DFP) variable-metric method, the new method preserves the positive-definiteness of the approximating matrix. Together with Greenstadt's method, the new method gives rise to a one-parameter family of variable-metric methods that includes the DFP an...

This paper explores the convergence of nonlinear conjugate gradient methods without restarts, and with practical line searches. The analysis covers two classes of methods that are globally convergent on smooth, nonconvex functions. Some properties of the Fletcher-Reeves method play an important role in the first family, whereas the second family shares an important property with the Polak-Ribir...

SARAH J. CADDICK, CHUNSHENG WANG, COLIN F. FLETCHER, NANCY A. JENKINS, NEAL G. COPELAND, AND DAVID A. HOSFORD Department of Neurology, Medical College of Virginia, Richmond, Virginia 23298; Department of Medicine, Division of Neurology and Department of Neurobiology, Duke University Medical Center and Durham Veterans Affairs Medical Center, Durham, North Carolina 27705; and Mammalian Genetics L...