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1.
In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.  相似文献   

2.
We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.  相似文献   

3.
In this paper,a modified version of Powell-Zangwill's method for function minimizationwithout calculating derivatives is proposed.The new method possesses following properties:quadratic termination,global convergence for strictly convex function and Q-linearconvergence rate for uniformly convex function.Furthermore,the main part of this paperis to show that the rate of convergence of the new method is quadratic for every n(2n 1)line searches if the objective function is a uniformly convex and suitably smooth functionon R~n.  相似文献   

4.
Trust region methods are powerful and effective optimization methods.The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods.The advantages of the above two methods can be combined to form a more powerful method for constrained optimization.The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound.At the same time,the new algorithm still possesses robust global properties.The global convergence of the new algorithm under standard conditions is established.  相似文献   

5.
A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G2 continuous spline approximation of conic section when using the subdivision scheme,and the effectiveness of this method is demonstrated by some numerical examples.  相似文献   

6.
The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.  相似文献   

7.
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.  相似文献   

8.
由同顺 《东北数学》2004,20(1):68-74
By combing the three-step modified method of characteristics and MMOCAA difference method with UNO interpolation, the three-step UNO-MMOCAA finite difference method is established for convection-dominated diffusion problems in this paper. The scheme is two-order accurate in space and time and is free from the oscillation near the steep front, with which the problem is solved by three-step MMOCAA finite difference method based on two-order Lagrange interplation. Using the new method, we give an estimate analysis of the scheme and a numerical example.  相似文献   

9.
A QP FREE FEASIBLE METHOD   总被引:22,自引:0,他引:22  
In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.  相似文献   

10.
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 (0 〈 dl ≤ m) and d2 (0 ≤ d2≤ n), builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.  相似文献   

11.
锥模型优化方法是一类非二次模型优化方法, 它在每次迭代中比标准的二次模型方法含有更丰富的插值信息. Di 和Sun (1996) 提出了解无约束优化问题的锥模型信赖域方法. 本文根据Fletcher 和Leyffer (2002) 的过滤集技术的思想, 在Di 和Sun (1996) 工作的基础上, 提出了解无约束优化问题的基于锥模型的过滤集信赖域算法. 在适当的条件下, 我们证明了新算法的收敛性. 有限的数值试验结果表明新算法是有效的.  相似文献   

12.
该文提出了一个基于二次三对角模型的直接搜索法.在通常的条件下,论文给出和证明了这个方法的收敛性.数值试验表明这个方法是较为有效的.  相似文献   

13.
A Conic Trust-Region Method for Nonlinearly Constrained Optimization   总被引:5,自引:0,他引:5  
Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.  相似文献   

14.
Geometry of interpolation sets in derivative free optimization   总被引:2,自引:0,他引:2  
We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods. These bounds involve a constant that reflects the quality of the interpolation set. The main task of such a derivative free algorithm is to maintain an interpolation sampling set so that this constant remains small, and at least uniformly bounded. This constant is often described through the basis of Lagrange polynomials associated with the interpolation set. We provide an alternative, more intuitive, definition for this concept and show how this constant is related to the condition number of a certain matrix. This relation enables us to provide a range of algorithms whilst maintaining the interpolation set so that this condition number or the geometry constant remain uniformly bounded. We also derive bounds on the error between the model and the function and between their derivatives, directly in terms of this condition number and of this geometry constant.  相似文献   

15.
已知结点处的函数值和一阶导数值,给出了构造一类二次分形插值函数的方法.不同于仿射分形插值函数,得到的插值函数具有可微性,并讨论分形插值函数的微积分运算,最后给出一个构造例子.  相似文献   

16.
1引言本文考虑的无约束最优化问题为(?)f(x),(1.1)其中f(x)为连续可微函数.解此问题的很多算法一般都采用二次函数模型去逼近f(x) ([10],[15]).对于一些非二次性态强、曲率变化剧烈的函数,用二次函数模型去逼近可能效果不好,因此Davidon于1980年首次提出了解无约束优化问题的锥模型方法.锥模型是二次模型的推广,比二次函数具有更多的自由度,因此期望能够更充分地逼近原函数.对于一些在极小点附近很不对称,或曲率变化剧烈的函数,或在某个区域内变化大的函数,全部或部分用锥模型去逼近的效果可能好于用二次模型去逼近.  相似文献   

17.
解线性约束优化问题的新锥模型信赖域法   总被引:1,自引:0,他引:1  
本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法.论文采用零空间技术消除了新锥模型子问题中的线性等式约束,用折线法求解转换后的子问题,并给出了解线性等式约束优化问题的信赖域方法.论文提出并证明了该方法的全局收敛性,并给出了该方法解线性等式约束优化问题的数值实验.理论和数值实验结果表明新锥模型信赖域方法是有效的,这给出了用新锥模型进一步研究非线性优化的基础.  相似文献   

18.
We consider some algorithms for unconstrained minimization without derivatives that form linear or quadratic models by interpolation to values of the objective function. Then a new vector of variables is calculated by minimizing the current model within a trust region. Techniques are described for adjusting the trust region radius, and for choosing positions of the interpolation points that maintain not only nonsingularity of the interpolation equations but also the adequacy of the model. Particular attention is given to quadratic models with diagonal second derivative matrices, because numerical experiments show that they are often more efficient than full quadratic models for general objective functions. Finally, some recent research on the updating of full quadratic models is described briefly, using fewer interpolation equations than before. The resultant freedom is taken up by minimizing the Frobenius norm of the change to the second derivative matrix of the model. A preliminary version of this method provides some very promising numerical results. Presented at NTOC 2001, Kyoto, Japan.  相似文献   

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