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带等式约束的光滑优化问题的一类新的精确罚函数 总被引:1,自引:0,他引:1
罚函数方法是将约束优化问题转化为无约束优化问题的主要方法之一. 不包含目标函数和约束函数梯度信息的罚函数, 称为简单罚函数. 对传统精确罚函数而言, 如果它是简单的就一定是非光滑的; 如果它是光滑的, 就一定不是简单的. 针对等式约束优化问题, 提出一类新的简单罚函数, 该罚函数通过增加一个新的变量来控制罚项. 证明了此罚函数的光滑性和精确性, 并给出了一种解决等式约束优化问题的罚函数算法. 数值结果表明, 该算法对于求解等式约束优化问题是可行的. 相似文献
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对于含约束不等式的最优化问题给出了一种双参数罚函数形式,在文[7]的拟牛顿算法的基础上提出了一个同时改变双参数罚函数的新算法,研究了它的收敛性,数值实验表明了该算法是有效的. 相似文献
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一般约束最优化拓广的强次可行方向法 总被引:5,自引:0,他引:5
本文讨论非线性等式与不等式最优化问题,引进一个拟罚函数及其相应的只带不等式约束的辅助问题,然后采用广义投影技术和强次可行方向法思想建立原问题的一个全局收敛新算法,该算法具有初点始任意,结构简单,计算量较小等特点。 相似文献
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介绍一种非线性约束优化的不可微平方根罚函数,为这种非光滑罚函数提出了一个新的光滑化函数和对应的罚优化问题,获得了原问题与光滑化罚优化问题目标之间的误差估计. 基于这种罚函数,提出了一个算法和收敛性证明,数值例子表明算法对解决非线性约束优化具有有效性. 相似文献
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《应用数学与计算数学学报》2017,(3)
针对非线性不等式约束优化问题提出一种新的光滑精确罚函数,并证明这种类型的光滑罚函数对求解非线性约束优化问题具有好的性质.基于这个光滑精确罚函数,文中设计罚函数算法,并证明在一些较弱的条件下,算法具有全局收敛性.最后,一些数值算例说明算法的有效性. 相似文献
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结合罚函数思想和广义梯度投影技术,提出求解非线性互补约束数学规划问题的一个广义梯度投影罚算法.首先,通过扰动技术和广义互补函数,将原问题转化为序列带参数的近似的标准非线性规划;其次,利用广义梯度投影矩阵构造搜索方向的显式表达式.一个特殊的罚函数作为效益函数,而且搜索方向能保证效益函数的下降性.在适当的假设条件下算法具有全局收敛性. 相似文献
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线性约束最优化问题的一族次可行方向法 总被引:1,自引:0,他引:1
简金宝 《高校应用数学学报(A辑)》1994,(2)
本文给出线性约束最优化问题的一族算法.方法具有如下特点:1)初始迭代点可以任意选取;2)一旦有某一个迭代点进入可行域,方法将成为一族可行方向法;3)算法避开不易处理的罚函数和罚参数.文中采用一种最优性控制函数将初始化阶段和最优化阶段有机地结合起来,正是这种技巧保证了算法的全局收敛性 相似文献
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In this paper, a new sequential penalty algorithm, based on the Linfin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm. 相似文献
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D. G. Luenberger 《Journal of Optimization Theory and Applications》1974,14(5):477-495
A new programming algorithm for nonlinear constrained optimization problems is proposed. The method is based on the penalty function approach and thereby circumyents the necessity to maintain feasibility at each iteration, but it also behaves much like the gradient projection method. Although only first-order information is used, the algorithm converges asymptotically at a rate which is independent of the magnitude of the penalty term; hence, unlike the simple gradient method, the asymptotic rate of the proposed method is not affected by the ill-conditioning associated with the introduction of the penalty term. It is shown that the asymptotic rate of convergence of the proposed method is identical with that of the gradient projection method.Dedicated to Professor M. R. HestenesThis research was supported by the National Science Foundation, Grant No. GK-16125. 相似文献
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提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的. 相似文献
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A penalty method for convex functions which cannot necessarily be extended outside their effective domains by an everywhere finite convex function is proposed and combined with the proximal method. Proofs of convergence rely on variational convergence theory. 相似文献
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A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization 总被引:2,自引:0,他引:2
Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising. 相似文献
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Hiroshi Yamashita 《Mathematical Programming》1982,23(1):75-86
The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved. 相似文献
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基于增广Lagrange函数的RQP方法 总被引:3,自引:0,他引:3
Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported. 相似文献
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不等式约束最优化的非光滑精确罚函数的一个光滑近似 总被引:2,自引:0,他引:2
为不等式约束最优化问题提出一个连续可微近似罚函数并研究它的性质.在此基础上,提出了两个罚函数方法并证明这两个方法是全局收敛的. 相似文献