THE SCHWARZ ALTERNATING METHOD FOR A FOURTH-ORDER VARIATIONAL INEQUALITY

In this paper the Schwarz alternating method for a fourth-order elliptic variational inequality problem is considered by way of the equivalent form, and the geometric convergence is obtained on two subdomains.     

隐式曲面与参数曲面的G3过渡

通过几何过渡方法，结合重新标度连续概念，利用隐式曲面与参数曲面的各自等距曲面的交线，构成隐式曲面与参数曲面问的过渡面．用曲面的隐式与隐式、参数与参数形式，证明了所作的过渡面与给出的隐式曲面与参数曲面在连接线处是G^3连接的。     

求广义几何规划全局最优解的线性化方法

对广义几何规划问题(GGP)提出了一个确定型全局优化算法，这类优化问题能广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中，使用指数变换及对目标函数和约束函数的线性下界估计，建立了GGP的松弛线性规划(RLP)，通过对RLP可行域的细分以及一系列RLP的求解过程，从理论上证明了算法能收敛到GGP的全局最优解，对一个化学工程设计问题应用本文算法，数值实验表明本文方法是可行的。     

Necessary optimality conditions for abnormal problems with geometric constraints

The abnormal minimization problem with a finite-dimensional image and geometric constraints is examined. In particular, inequality constraints are included. Second-order necessary conditions for this problem are established that strengthen previously known results.     

氏调制的几何布朗运动与布林带

在证券市场, 布林带作为流行的技术分析工具被广泛的运用\bd 到目前为止有许多模型被建立用来预测证券的价格, 因此研究这些模型是否具有布林带性质是一个重要的问题\bd Liu, Huang and Zheng (2006)和Liu and Zheng (2006)分别讨论了Black-Scholes模型和随机波动率模型作为真实的股票市场的布林带, 并且证明了相应的统计量的平稳性和大数定律成立\bd 本文我们将上述结果推广到马氏调制的几何布朗运动模型.     

The proof of hermann''s conjecture

This note proves Thomas Hermann's conjecture on the comparison between twoboundaries of the derivatives of rational cubic Bezier curves. The result is valuable for computer aided geometric design.     

A General Alternative Procedure for Solving Negative Degree of Difficulty Problems in Geometric Programming

The degree of difficulty is an important concept in classical geometric programming theory. The dual problem is often infeasible when the degree of difficulty is negative and little has been published on this topic. In this paper, an alternative procedure is developed to find the optimal solution for the posynomial geometric programming problem with a negative degree of difficulty. First an equivalent problem was constructed with a positive degree of difficulty and the general posynomial geometric programming problem was solved using an original method previously developed by the authors. This method avoids the difficulty of non-differentiability of the dual objective function in the classical methods classified as dual. It also avoids the problem that appears when the feasible region for the dual problem is formed by an inconsistent system of linear equations.     

An Efficient Algorithm for Generating Univariate Cubic L 1 Splines

An active set based algorithm for calculating the coefficients of univariate cubic L ₁ splines is developed. It decomposes the original problem in a geometric-programming setting into independent optimization problems of smaller sizes. This algorithm requires only simple algebraic operations to obtain an exact optimal solution in a finite number of iterations. In stability and computational efficiency, the algorithm outperforms a currently widely used discretization-based primal affine algorithm.     

基于对数灰关联度的加权几何平均组合预测模型的有效性

基于对数灰关联度的加权几何平均组合预测是一种新的非线性组合预测。针对该方法提出新的优性组合预测、预测方法优超、冗余度等概念,给出优性组合预测存在的充分条件,最后证明冗余预测方法的一个判定定理。