八硬币集中四坏硬币的最优测试方法

在前人研究成果的基础上,给出用无砝码的天平从8个硬币中搜索4枚坏硬币的最优搜索方法.     

保险赔付中的最优对冲策略

本文对带有付费过程$A_t$的保险公司在金融市场$(S_t,Q_t,B_t)$上通过购买股票$S_t$、兑换外币$Q_t$以及购买无风险资产$B_t$的投资过程而采取的最优投资策略, 使保险公司所面临的风险最小进行探讨. 利用Galtchouk-Kunita-Watanabe分解定理将风险表达式重新表达, 从而找到保险公司所能采取的风险最小的最优对冲策略. 文中举出一个具有现实性意义的例子将文章的重要结论加以应用, 使本文更具有应用价值.     

Kinetics of decomposition pathways of an energetic GZT molecule

This investigation uses the Gaussian 98 program, density functional theory (DFT) B3LYP/6‐31G(d,p), and ab initio MP2/6‐31G(d,p) and HF/6‐31G(d) methods to model energetic diguanidinium 5,5′‐azotetrazolate (GZT) ionic species in order to determine their decomposition mechanisms. GZT was initially cracked into two guanidinium cations (G⁺) and a 5,5′‐azotetrazolate anion (ZT^2?). Three routes—the elimination of a hydronium ion (H⁺), the elimination of a hydrogen radical (H·), and the elimination of an amine radical (·NH₂)—are suggested for the decomposition of the G⁺ cation, and three routes—single ring opening, double ring opening and N? N bond cleavage outside the ring—are proposed for the further decomposition of the ZT^2? anion. Fourteen decomposition species were obtained on splitting both the cation and anion. This result reveals the reliability of the aforementioned decomposition mechanisms. The transition state species were also obtained using a two‐structure or three‐structure synchronous transit‐guided quasi‐Newton (STQN) between the Cartesian coordinates of related particles at specific decomposition stages in this research. The corresponding activation energies in all decomposition stages were considered to infer the most feasible pathways of GZT decomposition. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Optimal shape design for the time‐dependent Navier–Stokes flow

This paper is concerned with the problem of shape optimization of two‐dimensional flows governed by the time‐dependent Navier–Stokes equations. We derive the structures of shape gradients for time‐dependent cost functionals by using the state derivative and its associated adjoint state. Finally, we apply a gradient‐type algorithm to our problem, and numerical examples show that our theory is useful for practical purposes and the proposed algorithm is feasible in low Reynolds number flows. Copyright © 2007 John Wiley & Sons, Ltd.     

Dual multilevel optimization

We study the structure of dual optimization problems associated with linear constraints, bounds on the variables, and separable cost. We show how the separability of the dual cost function is related to the sparsity structure of the linear equations. As a result, techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved in parallel. The performance of a multilevel implementation of the Dual Active Set algorithm is compared with CPLEX Simplex and Barrier codes using Netlib linear programming test problems.      

Rainfall forecasting by technological machine learning models

Accurate forecasting of rainfall has been one of the most important issues in hydrological research. Due to rainfall forecasting involves a rather complex nonlinear data pattern; there are lots of novel forecasting approaches to improve the forecasting accuracy. Recurrent artificial neural networks (RNNS) have played a crucial role in forecasting rainfall data. Meanwhile, support vector machines (SVMs) have been successfully employed to solve nonlinear regression and time series problems. This investigation elucidates the feasibility of hybrid model of RNNs and SVMs, namely RSVR, to forecast rainfall depth values. Moreover, chaotic particle swarm optimization algorithm (CPSO) is employed to choose the parameters of a SVR model. Subsequently, example of rainfall values during typhoon periods from Northern Taiwan is used to illustrate the proposed RSVRCPSO model. The empirical results reveal that the proposed model yields well forecasting performance, RSVRCPSO model provides a promising alternative for forecasting rainfall values.     

A filter-trust-region method for <Emphasis Type="Italic">LC</Emphasis><Superscript>1</Superscript> unconstrained optimization and its global convergence

In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative.We establish the global convergence of the algorithm under reasonable assumptions.     

A second-order method for unconstrained optimization

This paper presents a quadratically converging algorithm for unconstrained minimization. All the accumulation points that it constructs satisfy second-order necessary conditions of optimality. Thus, it avoids second-order saddle andinflection points, an essential feature for a method to be used in minimizing the modified Lagrangians in multiplier methods.The work of the first author was supported by NSF RANN AEN 73-07732-A02 and JSEP Contract No. F44620-71-C-0087; the work of the second author was supported by NSF Grant No. GK-37672 and the ARO Contract No. DAHCO4-730C-0025.     

An efficient algorithm for solving the discrete minisum problem

For a simple nonsmooth minimization problem, the discrete minisum problem, an efficient hybrid method is presented. This method consists of an ‘inner algorithm’ (Newton method) for solving the necessary optimality conditions and a gradient-type ‘outer algorithm’. By this way we combine the large convergence area of the gradient technique with the fast final convergence of the Newton method.