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961.
研究了可分离二次背包问题的一种直接算法.此类背包问题的目标函数是二次的,且含有严格的一次项,其不等式约束是线性的.给出所求模型的一般形式,经过预处理该模型,最终归为求解两类问题(P1)和(P2).重点是求解(P2)问题的最优解,通过分析(P2)问题的结构特点,假设固定一次项后问题的最优解和相应不等式的拉格朗日乘子已求出,通过比较拉格朗日乘子和(P2)问题的一次项系数来调节λ的大小,从而求出(P2)问题的最优解.对于(P1)问题,改进了Bretthauer和Shetty给出的算法(Bretthauer K M,Shetty B.A pegging algorithm for the nonlinear resource allocation problem.Computers and Operations Research,2002,29(5):505-527).此算法的计算复杂性为O(n).数值算例表明,将这种固定变量算法和文中的定理5结合起来,能够快速有效地求解此类更一般的二次背包问题. 相似文献
962.
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established. 相似文献
963.
The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported. 相似文献
964.
965.
966.
研究了Kenichiro提出的轮换对称形式的丢番图方程,即方程ab bc ca=ya+b+c3的求解问题,利用素数整除的一些性质,证明了该方程仅有平凡解a=b=c以及非平凡解(a,b,c)=(k,k,4k),(k,4k,k),(4k,k,k)(k∈N),从而完全解决了这个方程. 相似文献
967.
本文在Lp(1≤P〈+∞)空间上,研究了种群细胞增生中一类具扰动项的L—R模型,证明了这类模型相应的迁移算子生成半群的Dyson—Phillips展式的9阶余项R9(t)在L1空间上是弱紧和在Lp(1〈P〈+∞)空间上是紧的,从而获得了该迁移算子的谱在右半平面上仅由有限个具有限代数重数的离散本征值组成及该迁移方程解的渐近稳定性等结果. 相似文献
968.
The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in geometrical optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left(right)-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis. 相似文献
969.
Solvability of the Dirichlet Problem in W~(2,p )for a Class of Elliptic Equations with Singular Data
Loredana CASO 《数学学报(英文版)》2014,30(5):737-746
We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces. 相似文献
970.
Ji Qiang Zheng 《数学学报(英文版)》2014,30(4):547-566
In this paper,we study the global well-posedness and scattering problem for the energysupercritical Hartree equation iut+Δu.(|x|.γ.|u|2)u=0 with γ4 in dimension d γ.We prove that if the solution u is apriorily bounded in the critical Sobolev space,that is,u ∈Lt∞(I;Hxsc(Rd)) with sc:= γ/2.11,then u is global and scatters.The impetus to consider this problem stems from a series of recent works for the energy-supercritical nonlinear wave equation(NLW) and nonlinear Schrdinger equation(NLS).We utilize the strategy derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering is reduced to disprove the existence of three scenarios:finite time blowup;soliton-like solution and low to high frequency cascade.Making use of the No-waste Duhamel formula,we deduce that the energy of the finite time blow-up solution is zero and so get a contradiction.Finally,we adopt the double Duhamel trick,the interaction Morawetz estimate and interpolation to kill the last two scenarios. 相似文献