广义半无限规划问题的一种可行方向算法

基于Zoutendijk可行方向算法,本文提出了一种求解广义半无限规划问题的可行方向算法,在保证算法收敛的情况下,此算法比以往的算法在假设条件的要求上有着一定的优势,且数值试验表明此法是可行的.     

关于H.Yoshida的一个问题

H.Yoshida曾经提出下述问题:对级小于1/2的整函数f（z）,是否自原点出发的每一条射线,或者为它的Julia方向,或者在包含该射线的某个角域内当|z|→∞时有|f（z）|→∞.本文的结论表明对正则增长的整函数,H.Yoshida问题的答案是肯定的,而且对许多其他的Julia型方向,类似的问题的答案也是肯定的.     

Banach空间中余弦算子函数生成元的有界性

A是Banach空间X中余弦算子函数C（t),t∈R，和正弦算子函数S（t),t∈R，的生成元。本证明了，对每个f∈C（[0,T];X)，连续函数u,u(t)=∫-tS(t-s)f(s)ds,f∈[0,T]是二阶非齐次0初值问题，u″=Au f的强解的充要条件是：A是空间X中的有界算子。     

Dual decomposition of a single-machine scheduling problem

We design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0–1 linear program. Also, we show that upon termination of such an ascent direction algorithm we get a dual decomposition of the original problem, which can be exploited to develop approximative and enumerative approaches for it. Computational results exhibit that in our application the ascent direction leads to good Lagrangian lower and upper bounds.     

Norm-relaxed method of feasible directions for solving nonlinear programming problems

A variation of the Polak method of feasible directions for solving nonlinear programming problems is shown to be related to the Topkis and Veinott method of feasible directions. This new method is proven to converge to a Fritz John point under rather weak assumptions. Finally, numerical results show that the method converges with fewer iterations than that of Polak with a proper choice of parameters.     

An unconstrained optimization method using nonmonotone second order Goldstein's line search

In this paper,an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed.By using the negative curvature information from the Hessian, the sequence generated is shown to converge to a stationary point with the second order optimality conditions.Numerical tests on a set of standard test problems confirm the efficiency of our new method.     

Dimension-Splitting for Simplifying Diffusion in Lattice-Gas Models

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to each dimension, and with all dimensions treated identically. We show that the model resulting from this technique is equivalent to the macroscopic diffusion equation in the appropriate limit. This technique saves computational resources and reduces the complexity of model design, programming, debugging, simulation and analysis. For example, a reaction-diffusion simulation can be designed and tested as a one-dimensional system, and then directly extended to two or more dimensions. We illustrate the use of this approach in constructing a microscopically reversible model of diffusion-limited aggregation as well as in a model of growth of biological films.     

三维热传导型半导体问题的交替方向有限元方法

1　引　　言三维热传导型半导体器件瞬态问题的数学模型由四个非线性偏微分方程描述[1 ,2 ] ,记 Ω为 Ω=[0 ,1 ] 3的边界 ,三维问题-Δψ =α( p -e+ N( x) ) ,　　 ( x,t)∈Ω× [0 ,T] ,( 1 .1 ) e t= . ( De( x) e-μe( x) e ψ) -R( e,p,T) ,　 ( x,t)∈Ω× ( 0 ,T] ,( 1 .2 ) p t= . ( Dp( x) p +μp( x) p ψ) -R( e,p,T) ,　 ( x,t)∈Ω× ( 0 ,T] ,( 1 .3 )ρ( x) T t-ΔT =[( Dp( x) p +μp( x) p ψ) -( De( x) e-μe( x) e ψ) ] . ψ,　　　　　　 ( x,t)∈Ω× ( 0 ,T] . ( 1 .4 )ψ( x,t) =e( x,t) =p( …     

A variable-penalty alternating directions method for convex optimization

We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems. This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF Grants CCR-8907671, CDA-9024618 and CCR-9306807.