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| 1 | A Kernel Function Based Interior-Point Methods for Solving P_*(κ)-Linear Complementarity Problem显示文摘In this paper, motivated by the complexity results of Interior Point Methods (IPMs) forLinear Optimization (LO) based on kernel functions, we present a polynomial time IPM for solvingP_*(κ)-linear complementarity problem, using a new class of kernel functions. The special case of ournew class was considered earlier for LO by Y. Q. Bai et al. in 2004. Using some appealing propertiesof the new class, we show that the iteration bound for IPMs matches the so far best known theoreticaliteration bound for both large and small updates by choosing special values for the parameters of thenew class. | M.Reza PEYGHAMI Keyvan AMINI | 2010 | Acta Mathematica Sinica,English Series2010，26，9： | 2 |
| 2 | 一种非单调滤子信赖域算法解线性不等式约束优化显示文摘本文给出了一种新的多维滤子算法结合非单调信赖域策略解线性约束优化.目标函数及其投影梯度的分量组成了新的多维滤子,并且与信赖域半径有关.当信赖域半径充分小时,新的滤子能接受试探点,避免算法无限循环.非单调信赖域策略保证了新算法的整体收敛性.目前为止,多维滤子算法局部收敛性分析仍然没有解决,在合理假设下,我们分析了新算法的局部超线性收敛性.数值结果验证了算法的有效性. | 王珏钰 顾超 朱德通 | 2020 | 数学学报(中文版)2020，63，6： | 2 |
| 3 | Global and Local Convergence of a New Affine Scaling Trust Region Algorithm for Linearly Constrained Optimization显示文摘Chen and Zhang [Sci.China,Ser.A,45,1390–1397(2002)] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence.In this paper,we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization.Different from Chen and Zhang's work,the trial points generated by the new algorithm are accepted if they improve the objective function or improve the first order necessary optimality conditions.Under mild conditions,we discuss both the global and local convergence of the new algorithm.Preliminary numerical results are reported. | Chao GU De Tong ZHU | 2016 | Acta Mathematica Sinica,English Series2016，32，10： | 1 |
| 4 | 求解P_*(κ)-水平线性互补问题的核函数内点算法显示文摘提出了一个新的核函数,使用该核函数设计了一个求解P*(κ)-水平线性互补问题(P*(κ)-HLCP)的多项式内点算法.为了给出算法的复杂度,首先分析了该核函数的性质;最后,给出了大步更新算法和小步更新算法的迭代复杂度,这些复杂度与目前内点算法最好的复杂度一致. | 杨喜美 张因奎 裴永刚 | 2016 | 河南师范大学学报(自然科学版)2016，44，5： | 1 |
| 5 | 基于新的核函数求解线性规划的原始-对偶内点算法显示文摘基于一个新的不显含增长项与障碍项的核函数,对线性规划提出了一种原始-对偶内点算法。这个核函数用于确定算法的搜索方向和度量迭代点与中心路径的距离。基于新的核函数和相应邻近函数良好的分析性质,证明了大步校正和小步校正算法的迭代复杂性阶分别为O(nlogn/ε)和O(nlognε)。 | 袁贝贝 张明望 | 2016 | 南阳理工学院学报2016，8，6： | 1 |
| 6 | A Large-Update Feasible Interior-Point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function显示文摘In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel function.The goal of this paper is to investigate such a kernel function and show that the algorithm has the best complexity bound.The complexity bound is shown to be O(√n log n log n/∈). | B.Kheirfam F.Hasani | 2013 | Journal of the Operations Research Society of China2013，1，3： | 0 |
| 7 | Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems显示文摘In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper. | Imene TOUIL Wided CHIKOUCHE | 2022 | Acta Mathematicae Applicatae Sinica2022，38，1： | 0 |
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