约束Hamilton系统的积分因子及其守恒量

本文提出了约束Hamilton 系统守恒量构成的一般途径．首先,给出了约束Hamilton 系统的固有约束,并且建立了约束Hamilton 系统正则方程;其次,给出了约束Hamilton 系统的积分因子和守恒量定理;然后构建了约束Hamilton 系统的广义Killing 方程;最后举例说明其应用．显然,这种方法与之前的方法相比较,具有步骤清晰明了、限制条件少、运算简单的优点．     

Bilinear identities for the constrained modified KP hierarchy

In this paper, we mainly investigate an equivalent form of the constrained modified KP hierarchy: the bilinear identities. By introducing two auxiliary functions ρ and σ, the corresponding identities are written into the Hirota forms. Also, we give the explicit solution forms of ρ and σ.     

三值T门组合网络自动综合的理论和算法

利用具有补运算三值格代数系统和三值T代数系统的基本运算和主要性质,提出了基于三值逻辑函数简化不相交积之和形式的三值T门组合网络自动综合的一些理论问题和算法,并给出了应用实例.利用CMOS管电路实现了三值T门模块和应用实例中的三值T门组合网络.HSPICE仿真实验验证了所设计的三值T门组合网络逻辑功能正确,表明该算法是有效的.该方法易实现三值T门组合网络的自动综合.     

On minimax eigenvalue problems via constrained optimization

In this paper, we consider the problem of minimizing the maximum eigenvalues of a matrix. The aim is to show that this optimization problem can be transformed into a standard nonlinearly constrained optimization problem, and hence is solvable by existing software packages. For illustration, two examples are solved by using the proposed method.     

解非线性约束优化问题的依赖域算法

本文对一般非线性约束优化问题提出了一个信赖域算法,导出了等价的KKT条件.在试探步满足适当条件下,证明了算法的全局收敛性,并进行了数值试验.     

Conditions and Algorithm for Optimal Solution of Probabilistic Constrained Programming

1.IntroductionAsweknow,theerroralwaysexistsinmeasurementanditisnormallydistributed,soweconsideraprobabilisticconstrainedprogrammingasbelow:WhereAeRTxnisastochaJsticmatrix,A1)A2,...,A.aretherowsofAandeachAinormallydistributedwithmeanmiandcovariancematrixDi,BER"x"isdeterministicmatrix,xisann-dimensionaldecisionvariable,b,c,daredeterministicvectorsofdimensionrtnfmrespectively,pisconstantreliabilitylevel,1相似文献   

Role of copositivity in optimality criteria for nonconvex optimization problems

Second-order necessary and sufficient conditions for local optimality in constrained optimization problems are discussed. For global optimality, a criterion recently developed by Hiriart-Urruty and Lemarechal is thoroughly examined in the case of concave quadratic problems and reformulated into copositivity conditions.     

Orthogonality constrained general variational calculation of excited state wavefunctions and energies: A new strategy

A viable strategy is developed for the general variational calculation of excited state wavefunctions which are constrained to remainorthogonal to all the lower-lying states of the samesymmetry. A key element of the strategy is to employ the penalised functional procedure for enforcing the relevant orthogonality constraints and the method of steepest descent to locate the constrained minima with respect to all variables, linear as well as nonlinear. The workability of the algorithm is tested by applying the technique for the optimization of nonlinear parameters in trial functions for the 2s state of H atom and singlet 1s2s states of helium atom and some isoelectronic ions.     

Concave minimization via conical partitions and polyhedral outer approximation

An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.Parts of the present paper were accomplished while the author was on leave at the University of Florida.Parts of the present paper were completed while the author was on leave at the University of Trier as a fellow of the Alexander von Humboldt foundation.     

On the convergence,invariance, and related aspects of a modification of Huang's algorithm

We consider a certain generalization of the Huang family of updates and discuss, firstly, convergence, dependence on parameters, and descent property; secondly, invariance under nonlinear scaling, conjugacy of search directions, and possibility of achieving a better approximation of the inverse of the Hessian. The last three aspects are shown to be dependent on particular choices of parameters. A numerical experiment is presented comparing the performances of the usual and modified BFGS algorithms.The author is indebted to Professor D. H. Jacobson and Professor M. J. D. Powell for helpful discussions during the preparation of this paper.This work was partially supported by a grant from Control Data.