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31.
This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one. 相似文献
32.
We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems
do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives.
A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of
the equality constraints. 相似文献
33.
Elie Leopold 《Numerical Algorithms》2007,44(4):347-366
In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of
all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials
are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given
a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations
are given. 相似文献
34.
In this paper a class of impulsive differential inclusions is investigated. The existence of solution bundle is proved. And we also construct a nonlinear semigroup of operators on cb(E) (closed-bounded subset of E) to describe the set of attainable states. 相似文献
35.
Chin-Yuan Hu 《Journal of Mathematical Analysis and Applications》2007,328(1):201-219
Recently we established Matysiak and Szablowski's conjecture [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] about a lower bound of real-valued characteristic functions. In this paper, applying an alternative approach we are able to give explicitly the ranges of argument for which the obtained inequalities hold true for general characteristic functions. 相似文献
36.
This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived. 相似文献
37.
讨论了Fuzzy矩阵A的同解简化矩阵A^(2),指出陈贻源论文《解Fuzzy关系方程》中定量3的错误。研究Fuzzy矩阵方程的摄动问题,解决了汤服成(2000)提出的未解决问题。 相似文献
38.
Summary Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent
or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic
coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem
of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier
transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved.
The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated.
Received 20 March 2001; accepted for publication 18 October 2001 相似文献
39.
Th. Friedrich I. Kath A. Moroianu U. Semmelmann 《Journal of Geometry and Physics》1997,23(3-4):259-286
A nearly parallel G2-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G2-manifolds with large symmetry group and in particular all homogeneous nearly parallel G2-structures. 相似文献
40.
We investigate the propeties of differential algebras generated by an operator d satisfying the property dN = 0 instead of d2 = 0 as in the usual case. Several examples of realizations of such differential algebras are given, either in the context of ZN-graded N × N matrix algebras, or as a generalized differential calculus on manifolds. 相似文献