Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

An Extrapolated Parallel Subgradient Projection Algorithm with Centering Technique for the Convex Feasibility Problem

In this paper,we present an extrapolated parallel subgradient projection method with the centering technique for the convex feasibility problem,the algorithm improves the convergence by reason of using centering techniques which reduce the oscillation of the corresponding sequence.To prove the convergence in a simply way,we transmit the parallel algorithm in the original space to a sequential one in a newly constructed product space.Thus,the convergence of the parallel algorithm is derived with the help of the sequential one under some suitable conditions.Numerical results show that the new algorithm has better convergence than the existing algorithms.

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.

Approximate subgradient projection algorithm for convex feasibility problem

An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.

NONDESCENT SUBGRADIENT METHOD FOR NONSMOOTH CONSTRAINED MINIMIZATION

A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.

CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES

In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.

Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities

A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.

Modified Subgradient Extragradient Method for Variational Inequality Problems and Fixed Point Problems

Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.

Modified Subgradient Extragradient Method for Pseudomonotone Variational Inequalities

Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms.

Subgradient Extragradient Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Space

Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.

ε-super Effcient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space

In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.

SA213-SUPER304H超级不锈钢焊接工艺

该文通过对SA213-SUPER304H超级不锈钢在超超临界机组安装焊接过程中的技术管理经历,结合自己从事火力发电厂焊接技术工作积累的丰富经验及一定的工艺实验和理论知识,对该SA213-SUPER304H钢材进行了材料物理化学性能分析、焊接工艺难点分析以及相应的措施制定,从而对该超级不锈钢小径管的焊接工艺的选择、现场焊接施工中应注意的事项及应采取的措施等均有一定的探索,给以后火电安装工程中该类钢材的焊接积累和总结了一些宝贵的经验和数据,具有一定借鉴意义。

SA213-Super304H、HR3C钢焊接工艺评定试验

SA213-Super304H、HR3C钢作为新型奥氏体耐热钢已应用于国内超超临界机组中。文章介绍了此种钢的焊接性能,结合青海省火电工程公司承建项目,对此种钢的焊接工艺评定进行了试验研究,讨论了焊接方法和焊接工艺特点。

基于算力-能量全分布式在线共享的5G网络负荷管理策略

5G与边缘计算等信息基础设施海量部署造成运营商用电成本上升,需推动边缘网络与电网的能量互动以节能降本。现有研究重点关注边缘网络参与日前经济调度,未考虑可再生能源和网络流量双重随机性造成的网络能量供需不平衡问题。针对强随机环境下的网络负荷管理问题,提出面向虚拟化边缘网络的能量实时管理策略。首先,以网络用能成本最小化为目标,构建联合网络资源管理、储能充放电与能量共享模型。其次,针对未来网络信息未知无法直接求解的问题,提出基于随机对偶次梯度法的在线管理策略。然后,针对资源共享涉及运营商隐私问题,提出全分布式的计算资源与能量协同共享算法。最后,仿真验证表明,所提在线算法在无需先验知识的前提下有效减少了5G边缘网络的用能成本。

基于老化成本实时次梯度的异构储能系统功率分配策略

随着锂离子电池的商业化推广和混合储能技术的发展,规模化储能系统可能存在异构特性。组成异构储能系统的储能单元之间存在差异,对储能系统内部功率分配提出更高的要求。为降低异构储能系统运行过程中的老化成本,首先,给出基于循环的老化模型用于计算不同储能单元老化成本;然后,提出一种无差在线雨流计数法实现功率与循环映射关系的实时更新,并使用链式法则得到储能系统老化成本关于充放电功率的实时次梯度,基于次梯度计算功率分配权重;最后,提出一种基于分配权重的功率迭代分配算法,考虑储能单元的功率边界和荷电状态边界。对分期建设的储能系统参与二次调频的场景进行仿真,结果表明,所提策略相比常用的两种功率分配方法(基于最大功率和基于剩余能量的分配策略)能够分别降低8.08%和10.34%的老化成本。

求解分裂可行问题的次梯度投影松弛算法

在无限维Hilbert空间中,区别于现有许多算法中的正交投影,采用次梯度投影法,提出求解分裂可行问题的次梯度投影松弛算法,并利用次梯度算子的cutter性质以及分类讨论的思想,证明了次梯度投影松弛算法生成的序列弱收敛于分裂可行问题的解.

伪单调变分不等式解集与拟非扩张映射不动点集公共元的强收敛定理

在Hilbert空间中提出一种新的关于求解伪单调变分不等式问题的Tseng外梯度算法。在适当条件下,证明由此算法生成的迭代序列强收敛于伪单调变分不等式问题的解集与拟非扩张映射不动点集的公共元,并用数值实验说明所提算法的有效性。

在线社交网络中点阻塞策略下虚假信息关注度

在线社交网络中的信息影响着人们的观点或看法,混杂在其中的虚假信息必然对人们的判断和决策产生误导.人们对虚假信息的关注度越高就越容易受到虚假信息的误导,从而做出非理性甚至激进的行为.为构建和谐的网络生态环境,本文探索了点阻塞策略下虚假信息关注度最小化问题以及最小化用户被虚假信息激活时对虚假信息的总关注度.首先,考虑用户对虚假信息的关注度构建一个关注度级联模型,并借助库伦定律来刻画虚假信息扩散过程中用户对虚假信息关注度的演化.其次,证明了点阻塞策略下虚假信息关注度最小化问题的复杂性以及该问题目标集函数的非次模性和非超模性.然后,将关注度最小化问题转化为关注度下降最大化问题,借助离散函数的连续化技术以及集函数的凹闭合函数设计了一种近似投影次梯度算法.最后,在三个真实的数据集中验证了本文构造算法和模型的有效性,实验模拟结果表明了本文开发的算法优于现存的启发式算法,并且得出用户对虚假信息的关注度是影响虚假信息治理的重要因素.

解伪单调变分不等式的修正惯性次梯度外梯度法

针对实Hilbert空间中的伪单调变分不等式问题,将惯性法和黏性法相结合,构造了一种基于Armijo线性搜索的次梯度外梯度法.在没有Lipschitz连续性的假定下,给出了该算法生成的迭代序列的强收敛性.最后,通过数值实验说明了该算法是有效的.

多UAV辅助反向散射边缘计算网络能耗优化方案

为了改善通信过程中由于遮挡导致信号衰落及设备能量不足以支撑大数据传输的问题,提出一种多无人机(Unmanned Aerial Vehicle,UAV)辅助反向散射边缘计算(Mobile Edge Computing,MEC)网络能耗优化方案。该方案根据UAV与反向散射辅助MEC系统模型构建非凸优化问题,利用块坐标下降法(Block Coodinate Descent,BCD)和变量替换将非凸优化问题转化为凸问题,再利用拉格朗日对偶算法和次梯度算法对该凸问题进行迭代求解。基于连续凸近似(Successive Convex Approximation,SCA)算法优化UAV轨迹,以最小化用户设备与UAV的能耗加权和。仿真结果表明,所提方案在不同参数下均有效可靠,与固定所有UAV轨迹、固定通信UAV轨迹、固定功率UAV轨迹等3种方案相比,所提方案能够有效降低系统能耗。