Some New A Priori Estimates for Second-Order Elliptic and Parabolic Interface Problems

We present some new a priori estimates of the solutions to the second-order elliptic and parabolic interface problems. The novelty of these estimates lies in the explicit appearance of the discontinuous coefficients and the jumps of coefficients across the interface.     

On a Constrained Optimal Rule for Classification with Unknown Prior Individual Group Membership

We describe a formal approach to constructing the optimal classification rule for classification analysis with unknown prior probabilities ofKmultivariate normal populations membership. This is done by suggesting a balanced design for the classification experiment and by constructing the optimal rule under the balanced design condition. The rule is characterized by a constrained minimization of total risk of misclassification; the constraint of the rule is constructed by a process of equalization among expected utilities ofKpopulation conditional densities. The efficacy of the suggested rule is examined through numerical studies. This indicates that dramatic gains in the accuracy of classification result can be achieved in the case where little is known about the relative population sizes.     

The constrained equal loss rule in problems with constraints and claims

In this article I study how to distribute a resource among different agents claiming on it, according to the equal loss principle, when there are some constraints in the problem. I introduce one single-valued rule. Some properties of this rule are given as well as an axiomatic characterization.     

A Multigrid Scheme for Elliptic Constrained Optimal Control Problems

A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational performance of the present multigrid scheme allows to investigate bang-bang control problems.AMS Subject Classification: 49J20, 65N06, 65N12, 65N55Supported in part by the SFB 03 “Optimization and Control”     

约束优化问题的一个变尺度投影算法的全局收敛性

利用投影算子 PxΩ 建立了求解问题 ( P)的变尺度投影算法 ,并讨论了算法的全局收敛性 .     

求解约束优化问题的一种算法的改进

针对用遗传算法求解约束优化问题时,初始种群产生的方法进行了研究,提出了初始种群产生的一种新方法.实验证明,该方法较直接利用随机数产生初始种群的方法,具有更快的运算速度.     

Modification of the Banzhaf Value for Games with a Coalition Structure

In this paper we introduce a new coalitional value in the context of TU games with an a priori system of unions, which it is called the symmetric coalitional Banzhaf value. This value satisfies the property of symmetry in the quotient game, the quotient game property, and it is a coalitional value of Banzhaf. Several characterizations are provided and two political examples illustrate the differences with respect to the Owen value and the Banzhaf–Owen value.     

求解一类约束优化问题的Newton分裂算法

本文给出了求解一类约束优化问题的一个Newton分裂算法，并证明了算法的局部平方收敛性，该算法与已有算法相比，具有计算量小的特点，因而特别适合于求解大规模问题，为进一步降低算法的计算复杂性，我们结合Broyden算法，给出了两类Broyden类分裂算法。     

求解不等式约束优化问题的一个改进算法

本文改进了一个求解不等式约束优化问题的对偶算法，建立了一个相应的算法，进一步证明了该算法的收敛性．最后，给出数值结果以验证该算法的有效性。     

A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation;we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence.The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution,which allows us to find a priori a subdomain where the computed solution requires a further improvement.This subdomain is defined by the perturbation parameterε,the step-size of a uniform mesh in x,and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im- proving the solution.To solve the discrete problems aimed at the improvement of the solution,we use uniform meshes on the subdomains.The error of the numerical so- lution depends weakly on the parameterε.The scheme converges almostε-uniformly, precisely,under the condition N~(-1)=o(ε~v),where N denotes the number of nodes in the spatial mesh,and the value v=v(K) can be chosen arbitrarily small for suitable K.     

Backward Error Bounds for Constrained Least Squares Problems

We derive an upper bound on the normwise backward error of an approximate solution to the equality constrained least squares problem min _Bx=d b – Ax₂. Instead of minimizing over the four perturbations to A, b, B and d, we fix those to B and d and minimize over the remaining two; we obtain an explicit solution of this simplified minimization problem. Our experiments show that backward error bounds of practical use are obtained when B and d are chosen as the optimal normwise relative backward perturbations to the constraint system, and we find that when the bounds are weak they can be improved by direct search optimization. We also derive upper and lower backward error bounds for the problem of least squares minimization over a sphere: .     

Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

In this paper, the continuously differentiable optimization problem min{f（x） ： x∈Ω}, where Ω ∈ R^n is a nonempty closed convex set, the gradient projection method by Calamai and More （Math. Programming, Vol.39. P.93-116, 1987） is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x^k} of bounded. Moreover, it is shown that, when f（x） is pseudo-convex （quasiconvex） function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method.     

关于等高k-毛虫树的带宽

图的带宽问题是图论的一个重要课题。然而 ,即使对毛长不等的单毛虫树 ,其带宽问题也是NP_完全的。利用Chv偄ｔａｌ的直径型带宽下界为工具 ,我们可以确定等高k_毛虫树的带宽     

各向异性增长拟线性椭圆型方程广义解最大模的先验估计

本文我们第一次给出了几类各向异性增长拟线性椭圆型方程广义解的最大模的先验估计。     

Weak and Strong Optimality Conditions for Constrained Control Problems with Discontinuous Control

In recent years, sufficient optimality criteria and solution stability in optimal control have been investigated widely and used in the analysis of discrete numerical methods. These results were concerned mainly with weak local optima, whereas strong optimality has been considered often as a purely theoretical aspect. In this paper, we show via an example problem how weak the weak local optimality can be and derive new strong optimality conditions. The criteria are suitable for practical verification and can be applied to the case of discontinuous controls with changes in the set of active constraints.     

一类耗散的Hasegawa-Mima方程的整体解

Applying the integral a priori estimates method, the existence and uniqueness of the global solution for the dissipative Hasegawa-Mima equation with initial periodic boundary condition was proved.