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结合有效集和多维滤子技术的拟Newton信赖域算法(英文) 总被引:1,自引:0,他引:1
针对界约束优化问题,提出一个修正的多维滤子信赖域算法.将滤子技术引入到拟Newton信赖域方法,在每步迭代,Cauchy点用于预测有效集,此时试探步借助于求解一个较小规模的信赖域子问题获得.在一定条件下,本文所提出的修正算法对于凸约束优化问题全局收敛.数值试验验证了新算法的实际运行结果. 相似文献
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本文提出一个求解不等式约束优化问题的基于指数型增广Lagrange函数的信赖域方法.基于指数型增广Lagrange函数,将传统的增广Lagrange方法的精确求解子问题转化为一个信赖域子问题,从而减少了计算量,并建立相应的信赖域算法.在一定的假设条件下,证明了算法的全局收敛性,并给出相应经典算例的数值实验结果. 相似文献
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一类带非单调线搜索的信赖域算法 总被引:1,自引:0,他引:1
通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某... 相似文献
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信赖域算法是求解无约束优化问题的一种有效的算法.对于该算法的子问题,本文将原来目标函数的二次模型扩展成四次张量模型,提出了一个带信赖域约束的四次张量模型优化问题的求解算法.该方法的最大特点是:不仅在张量模型的非稳定点可以得到下降方向及相应的迭代步长,而且在非局部极小值点的稳定点也可以得到下降方向及相应的迭代步长,从而在算法产生的迭代点列中存在一个子列收敛到信赖域子问题的局部极小值点. 相似文献
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带非线性不等式约束优化问题的信赖域算法 总被引:1,自引:0,他引:1
借助于KKT条件和NCP函数,提出了求解带非线性不等式约束优化问题的信赖域算法.该算法在每一步迭代时,不必求解带信赖域界的二次规划子问题,仅需求一线性方程组系统.在适当的假设条件下,它还是整体收敛的和局部超线性收敛的.数值实验结果表明该方法是有效的. 相似文献
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本文对等式约束问题提出了一个种组合信赖域与拟牛顿算法。该算法的特点是若Lagrangian函数的近似Hessian阵在等式约束Jacobi阵的零空间正定的,则选择拟牛顿算法,否则用信赖域算法,在通常信赖域算法的收敛假设下,该文证明了组合算法的全局收敛性。 相似文献
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信赖域法是一种保证全局收敛性的优化算法,为避免Hessian矩阵的计算,基于拟牛顿校正公式构造了求解带线性等式约束的非线性规划问题的截断拟牛顿型信赖域法.首先给出了截断拟牛顿型信赖域法的构造过程及具体步骤;然后针对随机用户均衡模型中变量和约束的特点对算法进行了修正,并将多种拟牛顿校正公式下所得结果与牛顿型信赖域法的结果进行了比较,结果发现基于对称秩1校正公式的信赖域法更为合适.最后基于数值算例结果得到了一些在算法编程过程中的重要结论,对其它形式信赖域法的编程实现具有一定的参考意义. 相似文献
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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
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In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems. 相似文献
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等式与界约束非线性优化的信赖域增广Lagrangian算法 总被引:2,自引:0,他引:2
1.引 言本文讨论如下非线性约束优化问题:其中; 是Rn→R的可微函数, .记 问题(1.1)是非线性约束优化问题中的一类重要类型,事实上任一个非线性等式与不等式约束优化均可引入松驰变量转化为(1.1)的形式.因此(1.1)的求解是人们讨论的热点问 相似文献
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We propose a modified sequential quadratic programming method for solving mixed-integer nonlinear programming problems. Under
the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when in- or decrementing an integer
value, successive quadratic approximations are applied. The algorithm is stabilized by a trust region method with Yuan’s second
order corrections. It is not assumed that the mixed-integer program is relaxable or, in other words, function values are evaluated
only at integer points. The Hessian of the Lagrangian function is approximated by a quasi-Newton update formula subject to
the continuous and integer variables. Numerical results are presented for a set of 80 mixed-integer test problems taken from
the literature. The surprising result is that the number of function evaluations, the most important performance criterion
in practice, is less than the number of function calls needed for solving the corresponding relaxed problem without integer
variables. 相似文献
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A new inexact-restoration method for nonlinear programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is improved explicitly; in Phase 2, optimality is improved on a tangent approximation of the constraints. Trust regions are used for reducing the step when the trial point is not good enough. The trust region is not centered in the current point, as in many nonlinear programming algorithms, but in the intermediate more feasible point. Therefore, in this semifeasible approach, the more feasible intermediate point is considered to be essentially better than the current point. This is the first method in which intermediate-point-centered trust regions are combined with the decrease of the Lagrangian in the tangent approximation to the constraints. The merit function used in this paper is also new: it consists of a convex combination of the Lagrangian and the nonsquared norm of the constraints. The Euclidean norm is used for simplicity, but other norms for measuring infeasibility are admissible. Global convergence theorems are proved, a theoretically justified algorithm for the first phase is introduced, and some numerical insight is given. 相似文献
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Yigui Ou Author Vitae Qian Zhou Haichan Lin 《Journal of Computational and Applied Mathematics》2009,232(2):318-326
In this paper, a new trust region algorithm is proposed for solving unconstrained optimization problems. This method can be regarded as a combination of trust region technique, fixed step-length and ODE-based methods. A feature of this proposed method is that at each iteration, only a system of linear equations is solved to obtain a trial step. Another is that when a trial step is not accepted, the method generates an iterative point whose step-length is defined by a formula. Under some standard assumptions, it is proven that the algorithm is globally convergent and locally superlinear convergent. Preliminary numerical results are reported. 相似文献
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Ove Edlund 《BIT Numerical Mathematics》1997,37(1):13-23
A subproblem in the trust region algorithm for non-linear M-estimation by Ekblom and Madsen is to find the restricted step.
It is found by calculating the M-estimator of the linearized model, subject to anL
2-norm bound on the variables. In this paper it is shown that this subproblem can be solved by applying Hebden-iterations to
the minimizer of the Lagrangian function. The new method is compared with an Augmented Lagrange implementation. 相似文献