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In this paper, a new derivative free trust region method is developed basedon the conic interpolation model for the unconstrained optimization. The conic inter-polation model is built by means of the quadratic model function, the collinear scalingformula, quadratic approximation and interpolation. All the parameters in this model axedetermined by objective function interpolation condition. A new derivative free method isdeveloped based upon this model and the global convergence of this new method is provedwithout any information on gradient.  相似文献
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§1 引言 在无约束最优化问题中,一个形式简单,引人注目的方法是对称秩一校正方法,简称SR1方法,这个方法是1959年Davidon(参见)首次提出来的,以后它一直吸引着许多数学工作者对它进行研究和改进(参见,,)。 SR1方法具有一个重要的性质,即不需要寻查步骤便可获得二次终止性,这个重要  相似文献
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A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.  相似文献
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In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.  相似文献
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This paper represents an inexact sequential quadratic programming (SQP) algorithm which can solve nonlinear programming (NLP) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.  相似文献
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1. IntroductionConsider the following linearly constrained nonlinear programming problemwhere x e R", A E Rmxn and f E C2. We are interested in the case when n and m arelarge and when the Hessian matrix of f is difficult to compute or is dense. It is ajssumed thatA is a matrix of full row rank and that the level set S(xo) = {x: f(x) 5 f(xo), Ax ~ b} isnonempty and compact.In the past few years j there were two kinds of methods for solving the large-scaleproblem (1.1). FOr the one kind, pr…  相似文献
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