共查询到20条相似文献,搜索用时 109 毫秒
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提出求解含平衡约束数学规划问题(简记为MPEC问题)的熵函数法,在将原问题等价改写为单层非光滑优化问题的基础上,通过熵函数逼近,给出求解MPEC问题的序列光滑优化方法,证明了熵函数逼近问题解的存在性和算法的全局收敛性,数值算例表明了算法的有效性。 相似文献
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低阶精确罚函数的一种二阶光滑逼近 总被引:1,自引:0,他引:1
给出了求解约束优化问题的低阶精确罚函数的一种二阶光滑逼近方法,证明了光滑后的罚优化问题的最优解是原约束优化问题的ε-近似最优解,基于光滑后的罚优化问题,提出了求解约束优化问题的一种新的算法,并证明了该算法的收敛性,数值例子表明该算法对于求解约束优化问题是有效的. 相似文献
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在二阶拟牛顿方程的基础上,结合Zhang H.C.提出的非单调线搜索构造了一种求解大规模无约束优化问题的对角二阶拟牛顿算法.算法在每次迭代中利用对角矩阵逼近Hessian矩阵的逆,使计算搜索方向的存储量和工作量明显减少,为大型无约束优化问题的求解提供了新的思路.在通常的假设条件下,证明了算法的全局收敛性和超线性收敛性.数值实验表明算法是有效可行的. 相似文献
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非线性约束条件下一个超线性收敛的可行方法 总被引:3,自引:0,他引:3
在本文中,我们对非线性不等式约束条件下的非线性优化问题给出了一个新的SQP类可行方法.此算法不但结构简单、易于计算,并且在适当的假设条件下,我们证明了算法具有全局收敛性及超线性收敛性 相似文献
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求解log—最优组合投资问题的一个自适应算法及其理论分析 总被引:2,自引:0,他引:2
本文给出了一个求解log-最优组合投资问题的自适应算法,它是一个变型的随机逼近方法。该问题是一个约束优化问题,因此,采用基于约束流形的梯度上升方向替代常规梯度上升方向,在一些合理的假设下证明了算法的收敛性并进行了渐近稳定性分析。最后,本文将该算法应用于上海证券交易所提供的实际数据的log-最优组合投资问题求解,获得了理想的数值模拟结果。 相似文献
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为非线性l1问题的求解构造了光滑逼近函数.首先将非线性l1问题转化为等价的不可微优化问题;其次通过两步提出光滑逼近函数的一般性构造方法;最后进行了数值仿真.文中介绍了光滑逼近函数的有关性质,指出相关文献已有的光滑函数方法是本文的特例,并证明了方法的收敛性及有效性. 相似文献
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Hilbert空间中广义平衡问题和不动点问题的粘滞逼近法 总被引:1,自引:1,他引:0
在Hilbert空间,我们用粘滞逼近法建立了一迭代序列来逼近两个集合的公共点,这两个集合分别是广义平衡问题的解集和渐进非扩张映射的不动点集.我们表明这一迭代序列强收敛到这两个集合的公共点,而且这一公共点还是一变分不等式的解.用这一结果,还研究了三个强收敛问题和优化问题. 相似文献
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In this paper, we introduce an iterative scheme based on the extragradient approximation method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a mixed equilibrium problem, and the set of solutions of the variational inequality problem for a monotone L-Lipschitz continuous mapping in a real Hilbert space. Then, the strong convergence theorem is proved under some parameters controlling conditions. Applications to optimization problems are given. The results obtained in this paper improve and extend the recent ones announced by Wangkeeree [R. Wangkeeree, An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings, Fixed Point Theory and Applications (2008) 17. doi:10.1155/2008/134148. Article ID 134148], Kumam and Katchang [P. Kumam, P. Katchang, A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mappings, Nonlinear Anal. Hybrid Syst. (2009) doi:10.1016/j.nahs.2009.03.006] and many others. 相似文献
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《Operations Research Letters》2020,48(1):78-85
We study a cutting-plane method for semidefinite optimization problems, and supply a proof of the method’s convergence, under a boundedness assumption. By relating the method’s rate of convergence to an initial outer approximation’s diameter, we argue the method performs well when initialized with a second-order cone approximation, instead of a linear approximation. We invoke the method to provide bound gaps of 0.5–6.5% for sparse PCA problems with 1000s of covariates, and solve nuclear norm problems over 500 × 500 matrices. 相似文献
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Jian-Wen Peng 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6001-6010
In this paper, we introduce a new viscosity approximation scheme based on the extragradient method for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions to the variational inequality for a monotone, Lipschitz continuous mapping. Several convergence results for the sequences generated by these processes in Hilbert spaces were derived. 相似文献
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求解简单界约束优化问题的一种逐次逼近法 总被引:1,自引:1,他引:0
马昌凤 《高等学校计算数学学报》1999,21(2):170-177
1引言考虑变量带简单界约束的非线性规划问题:其中二阶连续可微,a=(a1,a2,…,an),b=(b1,b2,…,bn),+i=1,2,…,n.问题(1)不仅是实际应用中出现的简单界约束最优化问题,而且相当一部分最优化问题可以把变量限制在有意义的区间内(参见[1]).因此无论在理论方面还是在实际应用方面,都有研究此类问题并给出简便而有效算法的必要.假设f是凸函数,记g(x)=f(x),则由K-T条件,问题(1)可化为求解下面的非光滑方程组:显然,(2)等价于易证,(3)等价于求解下面的非光滑方程… 相似文献
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JINDE WANG 《运筹学学报》1998,(1)
1.IntroductionDistributionproblemsareofgreatimportanceinstochasticoptimizationandstatis-tics.Usuallythiskindofproblemscanbedescribedinthefollowingform:wheref(x,w)isafuncti0ndefinedonR"xflandSisasubsetin'R".Because0fc0mplexityoftheproblems,ingeneral,onecangetonlytheirapproximatesolutions.Thefollowingtypeofapproximationis0ftenused:Letuscall(2)thefirsttype0fapproximation.DenotebyZ(w),A(w)theoptima1valueandoptimalsolutionsetofproblem(1)respectivelyandbyZk(w),Ak(w)thecorrespondingonesofproblem(… 相似文献
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In this paper, we investigate the problem for finding the set of solutions for equilibrium problems, the set of solutions of the variational inequalities for k-Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in a Hilbert space. We introduce a new viscosity extragradient approximation method which is based on the so-called viscosity approximation method and extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Finally, we utilize our results to study some convergence problems for finding the zeros of maximal monotone operators. Our results are generalization and extension of the results of Kumam [P. Kumam, Strong convergence theorems by an extragradient method for solving variational inequalities and equilibrium problems in a Hilbert space, Turk. J. Math. 33 (2009) 85–98], Wangkeeree [R. Wangkeeree, An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings, Fixed Point Theory and Applications, 2008, Article ID 134148, 17 pages, doi:10.1155/2008/134148], Yao et al. [Y. Yao, Y.C. Liou, R. Chen, A general iterative method for an finite family of nonexpansive mappings, Nonlinear Analysis 69 (5–6) (2008) 1644–1654], Qin et al. [X. Qin, M. Shang, Y. Su, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, Nonlinear Analysis (69) (2008) 3897–3909], and many others. 相似文献
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Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP’s with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space. 相似文献
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P. E. Maingé 《Journal of Optimization Theory and Applications》2008,138(3):459-477
This paper deals with a viscosity iterative method, in real Hilbert spaces, for solving a system of variational inequalities
over the fixed-point sets of possibly discontinuous mappings. Under classical conditions, we prove a strong convergence theorem
for our method. The proposed algorithm can be applied for instance to solving variational inequalities in some situations
when the projection methods fail. Moreover, the techniques of analysis are novel and provide new tools in designing approximation
schemes for combined and bilevel optimization problems. 相似文献
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Viscosity Approximation Methods for Generalized Multi-Valued Nonexpansive Mappings with Applications
AbstractIn this article, we study viscosity approximation methods for generalized multi-valued nonexpansive mappings and we present some new results related to strong convergence, variational inequality, convex optimization, split and common split feasibility problems (SFPs). Some numerical computations are also presented to illustrate our results. 相似文献