共查询到20条相似文献,搜索用时 31 毫秒
1.
Global Solutions and Their Large-time Behavior of Cauchy Problem for Equations of Deep Water Type
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We consider the large time behavior of the global solution of the Cauchy problem for the equation of Benjamin-Ono type. A series of large-time global estimates for Cauchy problem arc constructed. By means of the obtained global estimates uniformly for 0 ≤ t < ∞, the attractors of the Cauchy problem for the mentioned nonlinear equations are considered. And also the dimensions of the global attractor are estimated. 相似文献
2.
This paper considers the nonlinearly constrained continuous global minimization problem. Based on the idea of the penalty function method, an auxiliary function, which has approximately the same global minimizers as the original problem, is constructed. An algorithm is developed to minimize the auxiliary function to find an approximate constrained global minimizer of the constrained global minimization problem. The algorithm can escape from the previously converged local minimizers, and can converge to an approximate global minimizer of the problem asymptotically with probability one. Numerical experiments show that it is better than some other well known recent methods for constrained global minimization problems. 相似文献
3.
We consider the generalized Nash equilibrium problem which, in contrast to the standard Nash equilibrium problem, allows joint
constraints of all players involved in the game. Using a regularized Nikaido-Isoda-function, we then present three optimization
problems related to the generalized Nash equilibrium problem. The first optimization problem is a complete reformulation of
the generalized Nash game in the sense that the global minima are precisely the solutions of the game. However, this reformulation
is nonsmooth. We then modify this approach and obtain a smooth constrained optimization problem whose global minima correspond
to so-called normalized Nash equilibria. The third approach uses the difference of two regularized Nikaido-Isoda-functions
in order to get a smooth unconstrained optimization problem whose global minima are, once again, precisely the normalized
Nash equilibria. Conditions for stationary points to be global minima of the two smooth optimization problems are also given.
Some numerical results illustrate the behaviour of our approaches. 相似文献
4.
The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method. 相似文献
5.
For a class of global optimization (maximization) problems, with a separable non-concave objective function and a linear constraint a computationally efficient heuristic has been developed.The concave relaxation of a global optimization problem is introduced. An algorithm for solving this problem to optimality is presented. The optimal solution of the relaxation problem is shown to provide an upper bound for the optimal value of the objective function of the original global optimization problem. An easily checked sufficient optimality condition is formulated under which the optimal solution of concave relaxation problem is optimal for the corresponding non-concave problem. An heuristic algorithm for solving the considered global optimization problem is developed.The considered global optimization problem models a wide class of optimal distribution of a unidimensional resource over subsystems to provide maximum total output in a multicomponent systems.In the presented computational experiments the developed heuristic algorithm generated solutions, which either met optimality conditions or had objective function values with a negligible deviation from optimality (less than 1/10 of a percent over entire range of problems tested). 相似文献
6.
本文应用对时间的一致先验估计,证明了一类具有周期边值条件的长短波方程组的整体吸引子的存在性. 相似文献
7.
非线性拟抛物型积分微分方程的初边值问题和初值问题 总被引:1,自引:0,他引:1
本文研究非线性拟抛物积分微分方程的初边值问题和初值问题。运用Galerkin方程结合能量估计证明了问题的整体强解的生存性、唯一性和稳定性,最后在一定条件下讨论了初边值问题整体解的不存在性和爆破问题。 相似文献
8.
A filled function method for constrained global optimization 总被引:1,自引:0,他引:1
In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function
is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of
filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a
filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization
problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained
global optimization problems. 相似文献
9.
Lian-Sheng Zhang 《计算数学(英文版)》1988,6(4):375-382
We give an approach for finding a global minimization with equality and inequality Constraints.Our approach is to construct an exact penalty function, and prove that the global minimal points of this exact penalty function are the primal constrained global minimal points. Thus we convert the problem of global constrained optimization into a problem of global unconstrained optimization. Furthermore, the integral approach for finding a global minimization for a class of discontinuous functions is used and an implementable algorithm is given. 相似文献
10.
V.I. Korobov S.S. Pavlichkov W.H. Schmidt 《Journal of Mathematical Analysis and Applications》2005,309(2):743-760
A solution of the global controllability problem for a class of nonlinear control systems of the Volterra integro-differential equations is presented. It is proven that there exists a family of continuous controls that solve the global controllability problem for this class. The constructed controls depend continuously on the initial and the terminal states. It makes possible to prove the global controllability of the uniformly bounded perturbations of these systems under the global Lipschitz condition for the unperturbed system with respect to the states and the controls. 相似文献
11.
证明一类6阶Boussinesq型方程Cauchy问题整体广义解和整体古典解的存在性和唯一性,给出解在有限时刻发生爆破的充分条件. 相似文献
12.
Yao-jun Ye 《高校应用数学学报(英文版)》2015,30(4):453-465
The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studiedThe existence of global solutions for this problem is proved by constructing a stable set, and obtain the asymptotic stability of global solutions by means of a difference inequality. 相似文献
13.
In this paper, the existence and the uniqueness of the global strong solution and the global classical solution for the Cauchy problem of the multidimensional generalized IMBq equation are proved. The nonexistence of the global solution for the Cauchy problem of the generalized IMBq equation is discussed. 相似文献
14.
In this paper a new method for the simulation of uncertain nonlinear discrete time systems is given. The problem of simulation is reformulated as an optimization problem. Using methods of global optimization, namely, interval analysis, the global solution to the optimization problem stated is computed. Derivatives of the objective function of the optimization problem are computed using methods of automatic differentiation. The presented approach is implemented on a SPARC Station using the language PASCAL-XSC. For a typical example simulation results are presented and discussed. 相似文献
15.
Error estimates for shooting methods in two-point boundary value problems for second-order equations
This paper is concerned with a procedure for estimating the global discretization error arising when a boundary value problem for a system of second order differential equations is solved by the simple shooting method, without transforming the original problem in an equivalent first order problem. Expressions of the global discretization error are derived for both linear and nonlinear boundary value problems, which reduce the error estimation for a boundary value problem to that for an initial value problem of same dimension. The procedure extends to second order equations a technique for global error estimation given elsewhere for first order equations. As a practical result the accuracy of the estimates for a second order problem is increased compared with the estimates for the equivalent first order problem. 相似文献
16.
Barbara Panicucci Massimo Pappalardo Mauro Passacantando 《Computational Optimization and Applications》2010,45(2):415-425
In this paper we propose a class of differentiable gap functions in order to formulate a generalized variational inequality
(GVI) problem, involving a set-valued map with closed and convex graph, as an optimization problem. We also show that under
appropriate assumptions on the set-valued map, any stationary point of the equivalent optimization problem is a global optimal
solution and solves the GVI. Finally, we describe descent methods for solving the optimization problem equivalent to the GVI
and we prove its global convergence. 相似文献
17.
18.
E. V. Radkevich 《Journal of Mathematical Sciences》2012,181(5):701-750
We continue the study of the global solvability of the Cauchy problem for discrete kinetic equations and consider the general
case of complex data of the problem. We prove the existence of a global solution and obtain its representation. Bibliography:
10 titles. 相似文献
19.
This work investigates the existence of globally Lipschitz continuous solutions to a class of initial-boundary value problem of quasilinear wave equations. Applying the Lax's method and generalized Glimm's method, we construct the approximate solutions of initial-boundary Riemann problem near the boundary layer and perturbed Riemann problem away from the boundary layer. By showing the weak convergence of residuals for the approximate solutions, we establish the global existence for the derivatives of solutions and obtain the existence of global Lipschitz continuous solutions of the problem. 相似文献
20.
Herbert Arndt 《Numerische Mathematik》1984,43(3):343-360
Summary Retarded initial value problems are routinely replaced by an initial value problem of ordinary differential equations along with an appropriate interpolation scheme. Hence one can control the global error of the modified problem but not directly the actual global error of the original problem. In this paper we give an estimate for the actual global error in terms of controllable quantities. Further we show that the notion of local error as inherited from the theory of ordinary differential equations must be generalized for retarded problems. Along with the new definition we are led to developing a reliable basis for a step selection scheme. 相似文献