Smoothing Newton Algorithm for Linear Programming over Symmetric Cones

By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.

EXTENSION OF SMOOTHING NEWTON ALGORITHMS TO SOLVE LINEAR PROGRAMMING OVER SYMMETRIC CONES

最近对在对称的锥上学习一些优化问题有许多兴趣。这份报纸在对称的锥(SCLP ) 上处理线性编程。这里的目的是扩大弄平牛顿算法解决 SCLP 的 Qi-Sun-Zhous，在用乔丹代数学的对称的锥的描述为我们的分析形成基本基础的地方。由使用欧几里德几何学的乔丹代数学的理论，作者证明算法是全球性并且局部地在合适的假设下面二次地会聚。解决秒顺序锥编程的初步的数字结果也被报导。

THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING

In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.

A New Infeasible-Interior-Point Algorithm Based on Wide Neighborhoods for Symmetric Cone Programming

In this paper,we present an infeasible-interior-point algorithm,based on a new wide neighborhood for symmetric cone programming.We treat the classical Newton direction as the sum of two other directions,and equip them with different step sizes.We prove the complexity bound of the new algorithm for the Nesterov-Todd(NT)direction,and the xs and sx directions.The complexity bounds obtained here are the same as small neighborhood infeasible-interior-point algorithms over symmetric cones.

Polynomial Convergence of Primal-Dual Path-Following Algorithms for Symmetric Cone Programming Based on Wide Neighborhoods and a New Class of Directions

This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direction is exactly the classical Newton direction.When the parameterθis independent of the rank of the associated Euclidean Jordan algebra,the algorithm terminates in at most O(κr logε−1)iterations,which coincides with the best known iteration bound for the classical wide neighborhood algorithms.When the parameterθ=√n/βτand Nesterov–Todd search direction is used,the algorithm has O(√r logε−1)iteration complexity,the best iteration complexity obtained so far by any interior-point method for solving SCP.To our knowledge,this is the first time that a class of interior-point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed over symmetric cone.

A Homogeneous Smoothing-type Algorithm for Symmetric Cone Linear Programs

In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.

考虑换相软开关三相不平衡调节的主动配电网多目标运行优化

由于三相负荷的日益不平衡,主动配电网中的功率损耗和三相电压相位不平衡问题日益严重。作为一种可取代传统联络开关的电力电子设备,智能软开关为减少网损与缓解不平衡问题提供了潜在方案。为此,引入三相四线制的背靠背电压源型变流器作为智能软开关的拓扑结构,同时针对该拓扑设计了相应的换相控制策略。在此基础上,提出了以减少网损和缓解电压不平衡度为优化目标的基于三相四线制换相软开关的主动配电网多目标优化运行模型;应用对称半定规划算法,通过凸松弛将原始非凸非线性模型转换为便于求解的半正定规划模型,该模型可对三相电网进行三相解耦与分析。最后,在改进的IEEE 123节点系统中进行案例研究,验证了所提模型及其求解算法的可行性和有效性。

计算对称群S_9的所有Sylow-p子群

利用Sylow-p子群的特性,通过设计有效的算法,给出了计算对称群S9的全部Sylow-p子群及其生成元的随机性算法,同时给出了计算的流程图及计算结果.

对称群元素的正规化子的计算

有限群的正规化子人工计算比较复杂,因此借助计算机辅助成为必要.根据郭旭初先生给出的对称群元素的正规化子的构造理论,设计出计算对称群任一元素的正规化子的算法,依此算法设计出相应的C语言程序,给出了计算示例.

对称群子集的正规闭包的生成算法及程序

根据正规闭包的意义及置换的运算特征,设计出对称群子集的正规闭包的生成算法,并且用C语言编写出相应的计算机程序.

回转对称非球面气囊抛光控制算法研究

介绍一种新型的非球面光学零件抛光方法———气囊抛光,这种方法可以得到高质量的光学表面。针对气囊抛光加工回转对称非球面的特点,进行抛光路径规划,对去除函数进行降维处理,提出抛光驻留时间的计算方法。最后,给出抛光算法的实现框图,并按照实现框图指导实际的玻璃非球面加工,取得满意结果,验证了算法的有效性。

构作纵横图的算法与计算机实现

根据“对称对换法”，给出了构作纵横图的算法及其相应的计算机程序，实现了构作纵横图的计算机化。

基于自适应参数校正策略求解SDP的Mehrotra型内点算法

最近,Salahi对线性规划提出了一个基于新的自适应参数校正策略的Mehrotra型预估-校正算法,该策略使其在不使用安全策略的情况下,证明了算法的多项式迭代复杂界.本文将这一算法推广到半定规划的情形.通过利用Zhang的对称化技术,得到了算法的多项式迭代复杂界,这与求解线性规划的相应算法有相同的迭代复杂性阶.

基于自适应参数校正策略求解SDP的二阶Mehrotra型内点算法

最近,Salahi提出了一种求解线性规划的基于自适应参数校正策略的二阶Mehrotra型预估-校正算法,并在不使用安全策略的情况下证明了其迭代的多项式复杂性。本文将这一算法推广到半定规划。通过利用Zhang的对称化技术,同样在不使用安全策略的情况下,证明了算法的多项式迭代复杂界。

A Note on a Recent Paper by J. S. Respondek

In this note, we give comments on a very recent paper by J. S. Respondek [1]. In [1], the author claims that an algorithm in [2] contains a severe error. We show that the algorithm in [2] can be implemented properly without causing any errors by using vectors (one-dimensional arrays) rather than using 2-dimensional arrays. To enable users and programmers of the algorithm to carry out the computations using all existing subscripts and superscripts in the algorithm, we give a correction in the first line of the algorithm. A Maple implementation for the algorithm, as it is in [2], is given as an example for symbolic programming.

A Cone Constrained Convex Program:Structure and Algorithms

In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and algorithms.We study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this problem.We then study some other approaches for solving this structured convex program.These include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program approach.Some numerical examples are presented.

对称锥规划的Mehrotra型预估-矫正算法的多项式复杂性（英文）

We establish polynomial complexity bounds of the Mehrotra-type predictorcorrector algorithms for linear programming over symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al[18]. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O(r log ε-1) iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.

组合优化（Ⅱ）——对称差分解法的又一应用

本文先讨论函数的增量与微分对于连续型最优化问题的作用，析出有益的启发。用之于组合优化，得到了求解问题的一个方法——对称差（的）分解法。文献［２］对它作了讨论并得到不少应用。本文提出两个赋权凸锥独立集合问题。它们是典型的组合优化问题，分别与线性规划中两个互为对偶模型等价；用对称差分解法进行求解。

对称锥规划的邻域跟踪算法

本文把艾文宝的邻域跟踪算法推广到对称锥规划,定义中心路径的宽邻域N(τ,β),并证明该邻域的一个重要性质,该性质在算法的复杂性分析中起到关键作用.取宽邻域N(τ,β)中一点为初始点并采用Nesterov-Todd(NT)搜索方向,则该算法的迭代复杂界为O(r(1/2)logε-1),其中,r是Euclid Jordan代数的秩,ε是允许误差.这是对称锥规划的宽邻域内点算法最好的复杂界.

局域非对称成分统治、句法加标与习语性领主句研究

基于层级性结构特征,汉语领主属宾句中领属义的句法实现方式归结于领有者和隶属者之间的非对称统治关系,而习语性领主句的推导生成则需要借助于复杂谓词的次范畴化选择要求。局部非对称统治是确保领主句形成领属关系的结构限制,与"N1的N2"的这种常规格式具有本质性差异。基于语段论中探针同时探测的分析说明,汉语习语性领主句符合非宾格假设的论元结构要求,其语义解读也需要参照话题、主语和题元三个拷贝成分才能完整地理解该句式。