Nonsingular systems of generalized Sylvester equations: An algorithmic approach

We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ?‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ?‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n³r) algorithm for computing the (unique) solution.     

A Penalized Likelihood Method for Classification With Matrix-Valued Predictors

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Factorizations of tropical and sign polynomials

In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call tropical polynomials and sign polynomials, respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polynomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials.     

艾拉姆咖分布参数变点的Bayes估计

研究了艾拉姆咖分布变点估计的非迭代抽样算法(IBF)和MCMC算法.在贝叶斯框架下,选取无信息先验分布,得到关于变点位置的后验分布和各参数的满条件分布,并且详细介绍了IBF算法和MCMC方法的实施步骤.最后进行随机模拟试验,结果表明两种算法都能够有效的估计变点位置,并且IBF算法的计算速度优于MCMC方法.     

线性权互补问题的新全牛顿步可行内点算法

基于一个连续可微函数,通过等价变换中心路径,给出求解线性权互补问题的一个新全牛顿步可行内点算法.该算法每步迭代只需求解一个线性方程组,且不需要进行线搜索.通过适当选取参数,分析了迭代点的严格可行性,并证明算法具有线性优化最好的多项式时间迭代复杂度.数值结果验证了算法的有效性.     

基于贝叶斯多元有序probit模型的休闲渔业游客满意度研究

游客满意度是休闲渔业景区制定管理决策的重要参考信息。通过探究游览过程中游客对各单一维度的满意程度与旅游总满意度之间的关系,管理者可以从中准确了解游客偏好、消费行为以及获取旅游产品设计等重要信息。据此,本文采取实地调研,获取11家全国休闲渔业示范基地1510份游客满意度信息,使用马尔科夫链蒙特卡洛法(Markov Chain Monte Carlo, MCMC),估算贝叶斯多元有序probit模型,并利用模型后验结果衡量休闲渔业游客7种分满意度对总体满意度的贡献。研究结果表明:渔憩体验满意度、景区环境满意度以及旅游餐饮满意度是对总体满意度影响程度最大的三种分满意度,所占比例分别为43.58%、24.67%、10.62%。     

考虑翻箱的场桥调度和提箱集卡数量的集成优化

在集装箱码头的进口箱堆场中,码头预约机制、待提箱的实时位置和场桥作业调度方案是制约堆场作业效率和堵塞情况的关键。为缓解进口箱堆场的拥塞情况并提高作业效率,在固定的预约时段内,考虑实时压箱量最少的翻箱规则,兼顾场桥间不可跨越和保持安全间距等现实约束,以场桥最长完工时间最小为目标,构建数学优化模型,设计了嵌入修复算子的改进遗传算法用于求解;通过算例实验验证了算法的有效性和方案的优越性,可为堆场实际作业提供决策参考。     

关于带运输的单机调度在线问题的研究

本文研究了带运输机的单机在线调度问题。问题假设工件实时在线到达,系统中有一台运输机,该运输机每次最多运输$k$个工件,每个工件需要先在单机上完成加工,然后再被运输机运往目的地,问题的优化目标为最小化完工时间,即所有工件被加工完并且运往目的地的时间最短。针对该问题,作者研究了工件满足一致性条件的模型,并且基于贪心思想给出了竞争比为$\frac{\sqrt{5}+1}{2}$的在线算法,并且证明该算法是最优在线算法。     

单机上带有可变前瞻区间的分批在线排序问题

本文研究单台无界平行批处理机上带有可变前瞻区间的在线排序问题。工件按时在线到达,目标是最小化时间表长。在时刻$t$,在线算法能够预见到$（t,t+\Delta（t）]$内到达工件的信息,这里前瞻区间的长度$\Delta（t）=\beta p_{\max}（t）$并非定长,其中$p_{\max}（t）$表示在$t$时刻及之前到达工件的最大加工时长,$\beta\in（0,1）$是常数。本文对于工件加工时长的一般情形,给出了当 0<β≤1/6 时最好可能的在线算法;对于工件加工时长被限制在一个区间的情形,给出了当 0<β<1 时最好可能的在线算法。