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101.
We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature. 相似文献
102.
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
103.
Laurent Bruneau 《Reports on Mathematical Physics》2004,54(2):169-199
We study Pauli-Fierz Hamiltonians-self-adjoint operators describing a small quantum system interacting with a bosonic field. Using quadratic form techniques, we extend the results of Dereziński-Gérard and Gérard about the self-adjointness, the location of the essential spectrum and the existence of a ground state to a large class of Pauli-Fierz Hamiltonians. 相似文献
104.
K. C. Kiwiel 《Journal of Optimization Theory and Applications》2007,134(3):549-554
We give a linear time algorithm for the continuous quadratic knapsack problem which is simpler than existing methods and competitive
in practice. Encouraging computational results are presented for large-scale problems.
The author thanks the Associate Editor and an anonymous referee for their helpful comments. 相似文献
105.
Rafael Caballero Mercedes González Flor M Guerrero Julián Molina Concepción Paralera 《European Journal of Operational Research》2007
In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant). 相似文献
106.
本针对P0函数互补问题,给出了一种微方程方法,并且证明了P0函数互补问题的解是微分方程系统的渐进稳定平衡点。在适当的假设条件下,证明了所给出的算法具有二次收敛速度。几个数值例子表明了该算法的有效性。 相似文献
107.
§ 1 IntroductionConsiderthefollowingnonlinearoptimizationproblem :minimizef(x)subjecttoC(x) =0 , a≤x≤b ,( 1 .1 )wheref(x) :Rn→R ,C(x) =(c1(x) ,c2 (x) ,...,cm(x) ) T:Rn→Rm aretwicecontinuouslydifferentiable,m≤n ,a ,b∈Rn.Trustregionalgorithmsareveryeffectiveforsolvingnonlinearoptimi… 相似文献
108.
Charles Blair 《Mathematical Programming》1995,71(2):127-136
We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients. 相似文献
109.
Q.J. Zhu 《Journal of Mathematical Analysis and Applications》2007,326(1):708-720
Investment systems are studied using a framework that emphasize their profiles (the cumulative probability distribution on all the possible percentage gains of trades) and their log return functions (the expected average return per trade in logarithmic scale as a function of the investment size in terms of the percentage of the available capital). The efficiency index for an investment system, defined as the maximum of the log return function, is proposed as a measure to compare investment systems for their intrinsic merit. This efficiency index can be viewed as a generalization of Shannon's information rate for a communication channel. Applications are illustrated. 相似文献
110.
首先将无线传感器网络的路由问题转化成求解最小Steiner树问题,然后给出了求解无线传感器网络路由的蚁群优化算法,并对算法的收敛性进行了证明.最后对找到最优解后信息素值的变化进行了分析.即在限制信息素取值的条件下,当迭代次数充分大时,该算法能以任意接近于1的概率找到最优解,并且当最优解找到后,最优树边上的信息素单调增加,而最优解以外边上的信息素在有限步达到最小值. 相似文献