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1.
本文提出了一种求解非线性约束优化的全局最优的新方法—它是基于利用非线性互补函数和不断增加新的约束来重复解库恩-塔克条件的非线性方程组的新方法。因为库恩-塔克条件是非线性约束优化的必要条件,得到的解未必是非线性约束优化的全局最优解,为此,本文首次给出了通过利用该优化问题的先验知识,不断地增加约束来限制全局最优解范围的方法,一些仿真例子表明提出的方法和理论有效的,并且可行的。  相似文献   

2.
We present a method, based on a variational problem, for solving a non-smooth unconstrained optimization problem. We assume that the objective function is a Lipschitz continuous and a regular function. In this case the function of our variational problem is semismooth and a quasi-Newton method may be used to solve the variational problem. A convergence theorem for our algorithm and its discrete version is also proved. Preliminary computational results show that the method performs quite well and can compete with other methods.  相似文献   

3.
We introduce a new method for solving an unconstrained optimization problem. The method is based on the solution of a variational inequality problem and may be considered a modified trust region algorithm. We prove the convergence of the method and present some numerical results.  相似文献   

4.
Our interest lies in solving sum of squares (SOS) relaxations of large-scale unconstrained polynomial optimization problems. Because interior-point methods for solving these problems are severely limited by the large-scale, we are motivated to explore efficient implementations of an accelerated first-order method to solve this class of problems. By exploiting special structural properties of this problem class, we greatly reduce the computational cost of the first-order method at each iteration. We report promising computational results as well as a curious observation about the behaviour of the first-order method for the SOS relaxations of the unconstrained polynomial optimization problem.  相似文献   

5.
This paper establishes a spectral conjugate gradient method for solving unconstrained optimization problems, where the conjugate parameter and the spectral parameter satisfy a restrictive relationship. The search direction is sufficient descent without restarts in per-iteration. Moreover, this feature is independent of any line searches. Under the standard Wolfe line searches, the global convergence of the proposed method is proved when |βk|βkFR holds. The preliminary numerical results are presented to show effectiveness of the proposed method.  相似文献   

6.
A direct second-variational algorithm is proposed for the iterative solution of optimal control problems in continuous, as well as discrete, systems. While the classical method using the Riccati transformation is shown to follow from the direct method, the latter has certain promising features in terms of structural simplicity, ease of programming, and substantial reduction in computation time. The process involves a predictor-corrector algorithm for a forward sweep in the state equations, followed by a backwards sweep in the adjoint equations. Applied to discrete systems, this method functions under conditions less stringent than in the classical scheme. Linearized quasioptimal feedback control is examined from the point of view of the direct method and a scheme for successive improvement in quasi-optimal policy is proposed for systems that suffer small perturbations from a given optimal trajectory.  相似文献   

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Chebyshev pseudo-spectral method is one of the most efficient methods for solving continuous-time optimization problems. In this paper, we utilize this method to solve the general form of shortest path problem. Here, the main problem is converted into a nonlinear programming problem and by solving of which, we obtain an approximate shortest path. The feasibility of the nonlinear programming problem and the convergence of the method are given. Finally, some numerical examples are considered to show the efficiency of the presented method over the other methods.  相似文献   

9.
An approach is proposed to the stable solution of discrete ill-posed problems on the basis of a combination of random projection of the initial ill-conditioned matrix with an ill-defined numerical rank and the pseudo-inversion of the resultant matrix. To select the dimension of the projection matrix, we propose to use criteria for the selection of a model and a regularization parameter. The results of experimental studies based on the well-known examples of discrete ill-posed problems are presented. Their solution errors are close to the Tikhonov regularization error, but a matrix dimension reduction owing to projection reduces the expenditures for computations, especially at high noise levels.  相似文献   

10.
A stochastic approximation algorithm is studied, in which random gradient estimates are averaged by an auxiliary, filter. Convergence of the algorithm is proved under a rather general noise condition. A practical version of the method is described and numerical results are given.  相似文献   

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12.
We consider NP-hard integer-valued multiindex problems of transportation type. We distinguish a subclass of polynomially solvable multiindex problems, namely multiindex problems with decomposition structure. We construct a general scheme for a heuristic method to solve a number of similar NP-hard decompositional multiindex problems. For one version of implementation for this scheme, we estimate its deviation from the optimum. We illustrate our results with the example of designing a class schedule.  相似文献   

13.
This paper presents a modified version of the water cycle algorithm (WCA). The fundamental concepts and ideas which underlie the WCA are inspired based on the observation of water cycle process and how rivers and streams flow to the sea. New concept of evaporation rate for different rivers and streams is defined so called evaporation rate based WCA (ER-WCA), which offers improvement in search. Furthermore, the evaporation condition is also applied for streams that directly flow to sea based on the new approach. The ER-WCA shows a better balance between exploration and exploitation phases compared to the standard WCA. It is shown that the ER-WCA offers high potential in finding all global optima of multimodal and benchmark functions. The WCA and ER-WCA are tested using several multimodal benchmark functions and the obtained optimization results show that in most cases the ER-WCA converges to the global solution faster and offers more accurate results than the WCA and other considered optimizers. Based on the performance of ER-WCA on a number of well-known benchmark functions, the efficiency of the proposed method with respect to the number of function evaluations (computational effort) and accuracy of function value are represented.  相似文献   

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Presents an efficient method for solving unconstrained optimization problems for nonlinear large mesh-interconnected systems. This method combines an approximate scaled gradient method with a block Gauss-Seidel with line search method which is used to obtain an approximate solution of the unconstrained quadratic programming subproblem. The authors prove that their method is globally convergent and demonstrate by several numerical examples its superior efficiency compared to a sparse matrix technique based method. In an example of a system of more than 200 variables, the authors observe that their method is 3.45 times faster than the sparse matrix technique based Newton-like method and about 50 times faster than the Newton-like method without the sparse matrix technique  相似文献   

17.
In this paper, we propose a parallel iterative method for calculating the extreme eigenpair (the largest or smallest eigenvalue and corresponding eigenvector) of a large symmetric tridiagonal matrix. It is based upon a divide and repeated, rank-one modification technique. The rank-one modification with a parameter only changes one diagonal element of each submatrix. We present a basic theory for subdividing the extremal eigenpair problem and then prove several convergence theorems that show the convergence of the iteration scheme for any positive initial modification parameter and the asymptotical quadratic convergence rate. Some numerical experiments are given, which show the efficiency of the parallel algorithm.  相似文献   

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This paper presents an implementation of an active-set line-search Newton method intended for solving large-scale instances of a class of multiple material minimum compliance problems. The problem is modeled with a convex objective function and linear constraints. At each iteration of the Newton method, one or two linear saddle point systems are solved. These systems involve the Hessian of the objective function, which is both expensive to compute and completely dense. Therefore, the linear algebra is arranged such that the Hessian is not explicitly formed. The main concern is to solve a sequence of closely related problems appearing as the continuous relaxations in a nonlinear branch and bound framework for solving discrete minimum compliance problems. A test-set consisting of eight discrete instances originating from the design of laminated composite structures is presented. Computational experiments with a branch and bound method indicate that the proposed Newton method can, on most instances in the test-set, take advantage of the available starting point information in an enumeration tree and resolve the relaxations after branching with few additional function evaluations. Discrete feasible designs are obtained by a rounding heuristic. Designs with provably good objective functions are presented.  相似文献   

20.
Results of numerical experiments in solving mass problems of determining membership of a set of points in a set of arbitrary shapes covering a domain or intersecting with each other in a space of arbitrary dimension are discussed. The problems are solved using geometrical techniques on graphics processors. The proposed solution can outperform the fastest classical algorithms by a factor from 6 to 700 in terms of speed. As an example, the construction of grids for computations within a geophysical model of the Earth is used. Such problems are typical for all the numerical computations involving geometric modeling where coverings or triangulations are used or rendering problems are solved.  相似文献   

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