新非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法

本文设计了求解无约束最优化问题的新的非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法.新的步长规则类似于Grippo非单调线搜索规则并包含Grippo非单调线搜索规则作为特例.新的步长规则在每一次线搜索时得到一个相对于Grippo非单调线搜索规则的较大步长,同时保证算法的全局收敛性.数值例子表明算法是有效的,适合求解大规模问题.     

An inexact secant algorithm for large scale nonlinear systems of equalities and inequalities

In this paper, an inexact secant algorithm in association with nonmonotone technique and filter is proposed for solving the large scale nonlinear systems of equalities and inequalities. The systems are transformed into a continuous constrained optimization solved by inexact secant algorithm. Global convergence of the proposed algorithm is established under the reasonable conditions. Numerical results validate the effectiveness of our approach.     

A new adaptive trust-region method for system of nonlinear equations

This study presents a new trust-region procedure to solve a system of nonlinear equations in several variables. The proposed approach combines an effective adaptive trust-region radius with a nonmonotone strategy, because it is believed that this combination can improve the efficiency and robustness of the trust-region framework. Indeed, it decreases the computational cost of the algorithm by decreasing the required number of subproblems to be solved. The global and the quadratic convergence of the proposed approach is proved without any nondegeneracy assumption of the exact Jacobian. Preliminary numerical results indicate the promising behavior of the new procedure to solve systems of nonlinear equations.     

Chaos expansion and asymptotic behavior of the Pareto distribution

We give the chaos expansion of a random variable with Pareto distribution and we analyze, by using the Malliavin calculus, the convergence in the distribution of a sequence of random variable with Pareto distribution toward the standard exponential law.     

Steffensen type methods for solving nonlinear equations

In the present paper, by approximating the derivatives in the well known fourth-order Ostrowski’s method and in a sixth-order improved Ostrowski’s method by central-difference quotients, we obtain new modifications of these methods free from derivatives. We prove the important fact that the methods obtained preserve their convergence orders 4 and 6, respectively, without calculating any derivatives. Finally, numerical tests confirm the theoretical results and allow us to compare these variants with the corresponding methods that make use of derivatives and with the classical Newton’s method.     

The Euler scheme and its convergence for impulsive delay differential equations

This paper presents a fixed stepsize Euler scheme for linear impulsive delay differential equations and considers its convergence. We propose a method to take the partition nodes for the Euler scheme. Employing the induction and the technique of inequality, we obtain the order of convergence for Euler scheme. An example is given to illustrate the efficiency of our result.     

On p-adic vector measure spaces

For a separating algebra R of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m:R→E a bounded finitely additive measure, we study some of the properties of the integrals with respect to m of scalar-valued functions on X. The concepts of convergence in measure, with respect to m, and of m-measurable functions are introduced and several results concerning these notions are given.     

Singular mixed boundary value problem

We study singular boundary value problems with mixed boundary conditions of the form

where , , f is a nonnegative function and satisfies the Carathéodory conditions on . Here, f can have a time singularity at t=0 and/or t=T and a space singularity at x=0 and/or y=0. We present conditions for the existence of solutions positive on [0,T) and having continuous first derivatives on [0,T].     

An analytic approximate method for solving stochastic integrodifferential equations

In this paper we compare the solution of a general stochastic integrodifferential equation of the Ito type, with the solutions of a sequence of appropriate equations of the same type, whose coefficients are Taylor series of the coefficients of the original equation. The approximate solutions are defined on a partition of the time-interval. The rate of the closeness between the original and approximate solutions is measured in the sense of the Lp-norm, so that it decreases if the degrees of these Taylor series increase, analogously to real analysis. The convergence with probability one is also proved.