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 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.

A Fixed-Point Iterative Method for Discrete Tomography Reconstruction Based on Intelligent Optimization

Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.

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。

基于样本优化的PPO算法在单路口信号控制的应用

优化交通信号的控制策略可以提高道路车辆通行效率,缓解交通拥堵.针对基于值函数的深度强化学习算法难以高效优化单路口信号控制策略的问题,构建了一种基于样本优化的近端策略优化(MPPO)算法的单路口信号控制方法,通过对传统PPO算法中代理目标函数进行最大化提取,有效提高了模型选择样本的质量,采用多维交通状态向量作为模型观测值的输入方法,以及时跟踪并利用道路交通状态的动态变化过程.为了验证MPPO算法模型的准确性和有效性,在城市交通微观模拟软件(SUMO)上与值函数强化学习控制方法进行对比.仿真实验表明,相比于值函数强化学习控制方法,该方法更贴近真实的交通场景,显著加快了车辆累计等待时间的收敛速度,车辆的平均队列长度和平均等待时间明显缩短,有效提高了单路口车辆的通行效率.

一种求解低秩矩阵补全的修正加速近端梯度算法

设计适应大规模数据的快速算法是求解低秩矩阵补全的重点。文章改变了加速近端梯度算法的步长,对近似函数的近端最优点和上一迭代点增加了一个仿射组合。通过控制仿射系数,能够使得到的新迭代点有靠近原函数的趋势,进而能在保持算法精度的同时提高算法效率。最后通过相应的数值实验证明了算法的有效性和稳定性。

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.

An Accelerated Proximal Gradient Algorithm for Hankel TensorCompletion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

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%。

一种基于稀疏优化和Nesterov动量策略的模型剪枝算法

随着深度学习快速发展,模型的参数量和计算复杂度爆炸式增长,在移动终端上部署面临挑战,模型剪枝成为深度学习模型落地应用的关键。目前,基于正则化的剪枝方法通常采用L2正则化并结合基于数量级的重要性标准,是一种经验性的方法,缺乏理论依据,精度难以保证。受Proximal梯度方法求解稀疏优化问题的启发,本文提出一种能够在深度神经网络上直接产生稀疏解的Prox⁃NAG优化方法,并设计了与之配套的迭代剪枝算法。该方法基于L1正则化,利用Nesterov动量求解优化问题,克服了原有正则化剪枝方法对L2正则化和数量级标准的依赖,是稀疏优化从传统机器学习向深度学习的自然推广。在CIFAR10数据集上对ResNet系列模型进行剪枝实验,实验结果证明Prox⁃NAG剪枝算法较原有剪枝算法性能有所提升。

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。

一种基于层接近度和分支距离函数的最优个体选择算法

文章针对目前最优个体评价及选择时存在的问题,在综合分析层接近度和分支距离函数特点的基础上,提出一种层接近度和分支距离函数联构的测试用例评价算法。该算法的基本思路是,在进化过程中选择领航个体时,先选择实际执行路径与目标路径接近度高的个体,再在这些个体集中选择分支距离最小的个体,从而得到领航能力最优的个体。实验结果表明,所提算法能快速寻优到测试用例,尤其是针对多层嵌套程序的测试用例,生成表现良好。

基于非Lipschitz步长策略的临近分裂可行问题的强收敛性研究

针对Hilbert空间中的临近分裂可行问题,该文提出了一种惯性粘滞类算法.其中主要引入了一种非Lipschitz步长策略,其克服了原步长远离零的缺点.另外,通过弱化临近映射的完全非扩张性,证明了修正后算法的强收敛性.进一步,将所得的结论应用于分裂均衡问题.最后,列举实例充分说明了修正后算法的有效性.

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。