PROXIMAL POINT ALGORITHM WITH ERRORS FOR GENERALIZED STRONGLY NONLINEARQUASIVARIATIONAL INCLUSIONS

In this paper, a class of generalized strongly nonlinear quasivariational inclusions are studied. By using the properties of the resolvent operator associated with a maximal monotone; mapping in Hilbert space, an existence theorem of solutions for generalized strongly nonlinear quasivariational inclusion is established and a new proximal point algorithm with errors is suggested for finding approximate solutions which strongly converge to the exact solution of the generalized strongly, nonlinear quasivariational inclusion. As special cases, some known results in this field are also discussed.

MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS FOR FINDING ROOTS OF MAXIMAL MONOTONE OPERATORS

In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.

Comparison of two approximal proximal point algorithms for monotone variational inequalities

Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequalities (MVI). Since solving the sub-problem exactly in each iteration is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we compare two APPA methods, both of which can be viewed as predic- tion-correction methods. The only difference is that they use different search directions in the correction-step. By extending the general forward-backward splitting methods, we obtain Algorithm I; in the same way, Algorithm II is proposed by spreading the general extra-gradient methods. Our analysis explains theoretically why Algorithm II usually outperforms Algorithm I. For computation practice, we consider a class of MVI with a special structure, and choose the extending Algorithm II to implement, which is inspired by the idea of Gauss-Seidel iteration method making full use of information about the latest iteration. And in particular, self-adaptive techniques are adopted to adjust relevant parameters for faster convergence. Finally, some nu- merical experiments are reported on the separated MVI. Numerical results showed that the extending Algorithm II is feasible and easy to implement with relatively low computation load.

On Over-Relaxed Proximal Point Algorithms for Generalized Nonlinear Operator Equation with (A,η,m)-Monotonicity Framework

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterative sequences generated by the algorithm are discussed. Our results improve and generalize the corresponding results in the literature.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

基于EMSDBO算法的无人机三维航迹规划

针对无人机(unmanned aerial vehicle,UAV)三维航迹规划问题,提出一种增强型多策略蜣螂算法的UAV航迹规划方法。首先,将飞行接近率和响应时间的动态约束添加到威胁成本代价中,并考虑UAV转弯性能的影响,建立三维任务空间模型与航迹代价函数。其次,在蜣螂算法中引入偏移估计策略、变螺旋搜索策略、准反向学习策略和逐维变异策略,提高算法的全局寻优能力和收敛速度。最后,给出了改进算法在三维环境下航迹规划的仿真结果。结果表明:综合考虑UAV机动性能和转弯性能,规划出的路径可以更加安全有效地避开危险源。相比其他算法,改进算法的寻优能力更好,规划的航迹质量更优。

基于注意力的循环PPO算法及其应用

针对深度强化学习算法在部分可观测环境中面临信息掌握不足、存在随机因素等问题,提出了一种融合注意力机制与循环神经网络的近端策略优化算法(ARPPO算法)。该算法首先通过卷积网络层提取特征;其次采用注意力机制突出状态中重要的关键信息;再次通过LSTM网络提取数据的时域特性;最后基于Actor-Critic结构的PPO算法进行策略学习与训练提升。基于Gym-Minigrid环境设计了两项探索任务的消融与对比实验,实验结果表明ARPPO算法较已有的A2C算法、PPO算法、RPPO算法具有更快的收敛速度,且ARPPO算法在收敛之后具有很强的稳定性,并对存在随机因素的未知环境具备更强的适应力。

基于混合启发式算法的中小学布局优化研究

以就近入学和均衡化发展为目标,提出中小学空间优化方法。从各区域学生平均上学距离与中小学空间分布的角度出发,建立武汉市中小学空间优化模型。基于ArcGIS分析和TS-SA混合启发式算法构建空间优化模型。经过学区优化调整,中小学可达规范服务半径内的能力得到提升,校际差异缩小,较好实现了就近入学、均衡教育和提升服务覆盖的目标。

基于强化学习的动目标协同观测任务自主规划方法

随着空间目标的数量逐渐增多、空中目标动态性日趋提升,对目标的观测定位问题变得愈发重要.由于需同时观测的目标多且目标动态性强,而星座观测资源有限,为了更高效地调用星座观测资源,需要动态调整多目标协同观测方案,使各目标均具有较好的定位精度,因此需解决星座协同观测多目标的任务规划问题.建立星座姿态轨道模型、目标飞行模型、目标协同探测及定位模型,提出基于几何精度衰减因子(geometric dilution of precision, GDOP)的目标观测定位误差预估模型及目标观测优先级模型,建立基于强化学习的协同观测任务规划框架,采用多头自注意力机制建立策略网络,以及近端策略优化算法开展任务规划算法训练.仿真验证论文提出的方法相比传统启发式方法提升了多目标观测精度和有效跟踪时间,相比遗传算法具有更快的计算速度.

异构编队卫星近距离操作轨迹规划方法

针对编队卫星的空间在轨服务任务,提出一种多类载荷异构星群的协同操作方案。首先,考虑星间自主通信,建立了由一颗主故障识别的观测卫星和多颗主维修补给的操作卫星构成的编队系统。其次,提出一种基于循环交替策略的多星协同轨迹规划方法,并基于差分进化算法优化了星群轨迹。最后,结合算例仿真,分析了系统内各成员卫星在编队控制过程中所需的脉冲大小以及编队系统整体的安全性能。仿真结果表明,异构编队系统可快速规划出安全性较高、鲁棒性较强的在轨服务轨迹,具有一定的工程应用价值。

基于Edge-TB的联邦学习中客户端选择策略和数据集划分研究

联邦学习是分布式机器学习在现实中的应用之一。针对联邦学习中的异构性,基于FedProx算法,提出优先选择近端项较大的客户端选择策略,效果优于常见的选择局部损失值较大的客户端选择策略,可以有效提高FedProx算法在异构数据和系统下的收敛速度,提高有限聚合次数内的准确率。针对联邦学习数据异构的假设,设计了一套异构数据划分流程,得到了基于真实图像数据集的异构联邦数据集作为实验数据集。使用开源的分布式机器学习框架Edge-TB作为实验测试平台,以异构划分后的Cifar10作为数据集,实验表明,采用新的客户端选择策略的改进FedProx算法较原算法在有限的聚合轮数内准确率提升14.96%,通信开销减小6.3%;与SCAFFOLD算法相比,准确率提升3.6%,通信开销减小51.7%,训练时间减少15.4%。

基于深度强化学习的尾旋改出技术

本文搭建了飞机仿真环境,基于近端策略优化(PPO)算法建立了尾旋改出算法测试模型,设计了基准版单阶段、基准版双阶段、加深版单阶段、加深版双阶段四种网络结构,用于探究网络结构和改出阶段对尾旋改出效果的影响,设置了鲁棒性测试试验,从时延、误差和高度等方面进行了算法测试和结果分析。

基于BB步长的近端随机递归动量算法

研究了一个求解非凸非光滑复合优化问题的算法。首先,结合近端随机递归动量算法和改进的BB步长,提出了一种带BB步长的随机方差缩减算法(ProxSTORM-BB)求解非凸非光滑复合优化问题。该算法在迭代过程中通过动态调节步长来提高算法的计算效率,并且对初始步长的选取不敏感,解决了参数调优比较困难这一问题。然后,在合适的假设条件下证明了算法的收敛性。最后,通过数值实验验证了算法的有效性。

脉冲负载下柴油发电机组建模优化与评价

针对柴油发电机组-三相不控整流器-DC/DC变换器-脉冲负载系统中柴油发电机组的输出特性,提出仿真模型与试验电源输出电压(流)波形契合度的评价指标,以判断模型的仿真程度;提出了基于反向(BP)传播神经网络算法的同步发电机励磁电压输出动态限幅方法,应用于脉冲负载下柴油发电机组的模型优化。试验验证表明:27组算例中,初始仿真模型有18组波形实时契合度值不足90%,优化仿真模型27组值均大于90%。说明本文提出的优化方法使仿真模型比初始模型更加有效,可应用于后续柴油发电机组带脉冲负载系统的研究。

基于邻近数据查询算法的街区路网规划仿真

城市街区路网的规划主要受到交通密度、主干路间隔的影响,由于交通环境的动态性,对路网的规划也需持续更新,因此通过路网规划获取最优出行路线难度较大。现提出基于邻近数据查询算法的街区路网规划方法。获取Voronoi图对街区路网空间数据集划分后的多个空间单元,并将其存储在路网结构中。基于空间均分法,将街区路网空间区域划分成不同的区域,利用邻近数据查询算法,查询路网目标节点。确定街区各个层次路网的规划拓展等级,建立街区路网拓扑树,通过对拓扑树获取街区路网最优路径节点序列,实现街区路网的规划。实验结果表明,研究方法完成路网规划时其最优路径查询时间、CPU开销以及路网规划耗时指标均优于对比方法,以此验证了提出方法具有更理想的实用性。

A Mini-Batch Proximal Stochastic Recursive Gradient Algorithm with Diagonal Barzilai–Borwein Stepsize

Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term.Proximal stochastic gradient methods are popular for solving such composite optimization problems.We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB,which incorporates the diagonal Barzilai–Borwein(DBB)stepsize strategy to capture the local geometry of the problem.The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions.We further establish the linear convergence of SRGDBB under the non-strong convexity condition.Moreover,it is proved that SRG-DBB converges sublinearly in the convex case.Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes.Furthermore,SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods.

Approximate Customized Proximal Point Algorithms for Separable Convex Optimization

Proximal point algorithm(PPA)is a useful algorithm framework and has good convergence properties.Themain difficulty is that the subproblems usually only have iterative solutions.In this paper,we propose an inexact customized PPA framework for twoblock separable convex optimization problem with linear constraint.We design two types of inexact error criteria for the subproblems.The first one is absolutely summable error criterion,under which both subproblems can be solved inexactly.When one of the two subproblems is easily solved,we propose another novel error criterion which is easier to implement,namely relative error criterion.The relative error criterion only involves one parameter,which is more implementable.We establish the global convergence and sub-linear convergence rate in ergodic sense for the proposed algorithms.The numerical experiments on LASSO regression problems and total variation-based image denoising problem illustrate that our new algorithms outperform the corresponding exact algorithms.

基于Jaro-Winkler算法的英语高效学习系统设计

针对传统英语教育课程效率低、资源单一的问题,文章结合Jaro-Winkler算法,应用浏览器/服务器(Browser/Server,B/S)架构和Java开发框架构建一个英语高效学习系统。该系统可实现单词形态相似度的计算,对库中词汇进行近形词的自动抽取,并在测验中将该近形词作为干扰选项,使单词的学习和测验更具有针对性。实验结果证明,该系统能够有效提高用户学习英语的效率、记忆词汇的准确性,能为用户提供一个高效、便捷的英语学习平台。

Improved pruning algorithm for Gaussian mixture probability hypothesis density filter

With the increment of the number of Gaussian components, the computation cost increases in the Gaussian mixture probability hypothesis density(GM-PHD) filter. Based on the theory of Chen et al, we propose an improved pruning algorithm for the GM-PHD filter, which utilizes not only the Gaussian components’ means and covariance, but their weights as a new criterion to improve the estimate accuracy of the conventional pruning algorithm for tracking very closely proximity targets. Moreover, it solves the end-less while-loop problem without the need of a second merging step. Simulation results show that this improved algorithm is easier to implement and more robust than the formal ones.

A CLASS OF COLLINEAR SCALING ALGORITHMS FOR UNCONSTRAINED OPTIMIZATON

A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.