共查询到19条相似文献,搜索用时 156 毫秒
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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
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本文给出半无限规划的一个对偶罚函数模型,该模型能处理目标函数不是凸函数的情形,从而凸(SIP)对偶为该模型的一个特例.并且,作为罚函数,本模型的罚因子比l1-罚函数要小,这使得算法更可行,最后,给出零对偶间隙证明. 相似文献
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借助于两套有限元网格空间提出了一种求解定常不可压Stokes方程的两层罚函数方法.该方法只需要求解粗网格空间上的Stokes方程和细网格空间上的两个易于求解的罚参数方程(离散后的线性方程组具有相同的对称正定系数矩阵).收敛性分析表明粗网格空间相对于细网格空间可以选择很小,并且罚参数的选取只与粗网格步长和问题的正则性有关.因此罚参数不必选择很小仍能够得到最优解.最后通过数值算例验证了上述理论结果,并且数值对比可知两层罚函数方法对于求解定常不可压Stokes方程具有很好的效果. 相似文献
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本文给出了广义可微精确罚函数的概念及一类所谓广义限域可微精确罚函数.本文预先选定罚因子,将不等式约束问题化为单一的无约束问题,并给出了具全局收敛性的算法.本文的罚函数构造简单,假设条件少而且算法的构造与收敛性结果是独特的. 相似文献
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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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Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods. 相似文献
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《Optimization》2012,61(3):353-374
In the present paper some barrier and penalty methods (e.g. logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex problems are studied, in particular, the radius of convergence of Newton’s method depending on the barrier and penalty para-meter is estimated, Unlike using self-concordance properties the convergence bounds are derived by direct estimations of the solutions of the Newton equations. The obtained results establish parameter selection rules which guarantee the overall convergence of the considered barrier and penalty techniques with only a finite number of Newton steps at each parameter level. Moreover, the obtained estimates support scaling method which uses approximate dual multipliers as available in barrier and penalty methods 相似文献
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г—环的单位元是其算子环中的元素.本文探讨Г—的单位与其算子环的单位元之间的关系.举例表明存在Г—环(ГN—环)M,它的左、右算子环均有单位元,而M既无左单位元,又无右单位元.那么在什么条件下,Г—环(ГN—环)的左、右算子环具有单位元时,其本身必定具有左、右单位元呢?对Г—环和ГN—环分别探讨了此问题,并给出了了解答此问题的充要条件. 相似文献
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Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms 总被引:1,自引:0,他引:1
We study five penalty function-based constraint handling techniques to be used with genetic algorithms in global optimization. Three of them, the method of superiority of feasible points, the method of parameter free penalties and the method of adaptive penalties have already been considered in the literature. In addition, we introduce two new modifications of these methods. We compare all the five methods numerically in 33 test problems and report and analyze the results obtained in terms of accuracy, efficiency and reliability. The method of adaptive penalties turned out to be most efficient while the method of parameter free penalties was the most reliable. 相似文献
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Zengxin Wei 《应用数学学报(英文版)》1992,8(3):281-288
The main difficulties encountered in the successive quadratic programming methods are the choice of penalty parameter, the choice of steplenth, and the Maratos effect. An algorithm without penalty parameters is presented in this paper. The choice of steplength parameters is based on the method of trust region. Global convergence and local superlinear convergence are proved under suitable assumption. 相似文献
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B. Prasad 《Journal of Optimization Theory and Applications》1981,35(2):159-182
A class of generalized variable penalty formulations for solving nonlinear programming problems is presented. The method poses a sequence of unconstrained optimization problems with mechanisms to control the quality of the approximation for the Hessian matrix, which is expressed in terms of the constraint functions and their first derivatives. The unconstrained problems are solved using a modified Newton's algorithm. The method is particularly applicable to solution techniques where an approximate analysis step has to be used (e.g., constraint approximations, etc.), which often results in the violation of the constraints. The generalized penalty formulation contains two floating parameters, which are used to meet the penalty requirements and to control the errors in the approximation of the Hessian matrix. A third parameter is used to vary the class of standard barrier or quasibarrier functions, forming a branch of the variable penalty formulation. Several possibilities for choosing such floating parameters are discussed. The numerical effectiveness of this algorithm is demonstrated on a relatively large set of test examples.The author is thankful for the constructive suggestions of the referees. 相似文献
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Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities 总被引:2,自引:0,他引:2
The alternating direction method is one of the attractive approaches for solving linearly constrained separate monotone variational inequalities. Experience on applications has shown that the number of iterations depends significantly on the penalty parameter for the system of linear constraint equations. While the penalty parameter is a constant in the original method, in this paper we present a modified alternating direction method that adjusts the penalty parameter per iteration based on the iterate message. Preliminary numerical tests show that the self-adaptive adjustment technique is effective in practice. 相似文献
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SHIDONGYANG 《高校应用数学学报(英文版)》1998,13(1):53-58
a special penalty method is presented to improve the accuracy of the standard penaltymethod (or solving Stokes equation with nonconforming finite element, It is shown that thismethod with a larger penalty parameter can achieve the same accuracy as the staodaxd methodwith a smaller penalty parameter. The convergence rate of the standard method is just hall order of this penalty method when using the same penalty parameter, while the extrapolationmethod proposed by Faik et al can not yield so high accuracy of convergence. At last, we alsoget the super-convergence estimates for total flux. 相似文献
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A new and universal penalty method is introduced in this contribution. It is especially intended to be applied in stochastic metaheuristics like genetic algorithms, particle swarm optimization or ant colony optimization. The novelty of this method is, that it is an advanced approach that only requires one parameter to be tuned. Moreover this parameter, named oracle, is easy and intuitive to handle. A pseudo-code implementation of the method is presented together with numerical results on a set of 60 constrained benchmark problems from the open literature. The results are compared with those obtained by common penalty methods, revealing the strength of the proposed approach. Further results on three real-world applications are briefly discussed and fortify the practical usefulness and capability of the method. 相似文献