基于几何非协调分解的Lagrange乘子区域分解方法

本文考虑将Lagrange乘子区域分解方法应用于几何非协调分解的情况来求解二阶椭圆问题.由于采用几何非协调区域分解,每个局部乘子空间关联到多个界面,我们按照一定的规则选取合适的乘子面来定义乘子空间.利用局部正则化技巧,可以消去内部变量,得到关于Lagrange乘子的界面方程.采用一种经济的预条件迭代方法求解界面方程,且相关的预条件子是可扩展的.     

从常步长梯度方法的视角看不可微凸优化增广Lagrange方法的收敛性

增广Lagrange方法是求解非线性规划的一种有效方法.从一新的角度证明不等式约束非线性非光滑凸优化问题的增广Lagrange方法的收敛性.用常步长梯度法的收敛性定理证明基于增广Lagrange函数的对偶问题的常步长梯度方法的收敛性,由此得到增广Lagrange方法乘子迭代的全局收敛性.     

基于MAS的多模式分布式资源约束多项目调度

针对实践中分布式多项目的活动往往具有多种执行模式,提出多模式分布式资源约束多项目调度问题。在项目动态到达环境下,考虑活动不同的执行模式,以工期最短和多项目延期成本最小为目标分别构建局部单项目调度模型和全局多项目决策模型,采用改进变邻域搜索算法求解初始局部调度计划,并设计基于模式调整的全局协商调度算法求解全局决策模型,通过双层算法实现分布式多项目调度中局部单项目调度与全局多项目调度系统性协调,减少项目中断和多项目延期成本。基于构建的多模式测试集进行的多项目数值实验表明：本文设计的双层算法可有效求解多模式分布式多项目调度问题,并且对不同规模问题求解具有良好的适应性。     

具有梯度限制的四阶障碍问题的增广Lagrange迭代方法

基于加罚方法和增广Lagrange泛函, 本文给出了一种求解具有梯度限制的四阶障碍问题的增广Lagrange迭代方法, 并证明了算法的收敛性.通过采用非协调有限元离散的数值实验表明, 该算法是行之有效的.     

一类不定性多人两层多目标协调决策模型的初探

考虑到组织决策中分权的普遍存在和高低管理层间依靠信息沟通所发生的控制和协调行为以及组织环境和内部条件的真实特征-不定性，本文将一类特殊的多人两层多目标协调决策模型置于组织不定性环境中予以研究，提出了不定性多人两层多目标协调决策模型．并通过模型的不断转化和K—T条件的应用，最终转化为确定的一般目标规划模型．同时，考虑到上层决策单元对下层决策行为的信息反馈进行处理时的及时性和交互性要求，一个具有快速反应能力的双层人机交互决策模式在问题求解中被设计出来以适应组织对适时目标管理的信息处理需要．     

带有不等式约束的非线性规划问题的一个精确增广Lagrange函数

对求解带有不等式约束的非线性非凸规划问题的一个精确增广Lagrange函数进行了研究．在适当的假设下,给出了原约束问题的局部极小点与增广Lagrange函数,在原问题变量空间上的无约束局部极小点之间的对应关系．进一步地,在对全局解的一定假设下,还提供了原约束问题的全局最优解与增广Lagrange函数,在原问题变量空间的一个紧子集上的全局最优解之间的一些对应关系．因此,从理论上讲,采用该文给出的增广Lagrange函数作为辅助函数的乘子法,可以求得不等式约束非线性规划问题的最优解和对应的Lagrange乘子．     

两类逼近精确罚函数法及其数值试验

1 引言 精确罚函数(exact penalty function)的构造主要有两条途径:一是基于Lagrange乘子的乘子罚函数方法,二是直接构造非光滑的精确罚函数。不必进行乘子迭代。本文讨论第三种思路:基于目标函数最优值构造保持光滑性的精确罚函数。某些无参数外点罚函数本应属于此类,但一直仅仅被作为普通外点罚函数的无参数形式。将其与无参 数内点罚函数同等看待,因此基于目标函数最优值构造精确罚函数未得到充分研究。文献[11]给出了初步结果。本文进一步发展了有关理论,导出了两类算法,证明了收敛性,最后给出了数值试验结果。 2 基于目标函数最优值的精确罚函数 考虑如下约束优化问题     

基于正弦控制因子的Lateral变异鲨鱼优化算法

针对传统鲨鱼优化算法在求解高维目标函数时,易早熟收敛,陷入局部最优的缺陷.提出一种基于正弦控制因子的Lateral变异鲨鱼优化算法.通过正弦曲线的特性和自适应惯性权重,改善了传统鲨鱼优化算法中由于随机选取控制因子数值大小可能导致算法在迭代后期全局搜索能力降低的问题,提高了算法在迭代后期的全局收敛能力,并对最佳鲨鱼位置引入Lateral变异策略,加强了算法跳出局部最优的可能性.改进后的算法对多个shifted单峰,多峰以及固定维测试函数进行求解,实验结果表明,对比多种不同优化算法而言,本文所提LSSO算法具有更高的收敛精度和搜索速度.     

线性约束两分块非凸优化的ADMM-SQP算法

基于乘子交替方向法(ADMM)和序列二次规划(SQP)方法思想, 致力于研究线 性约束两分块非凸优化的新型高效算法. 首先, 以SQP思想为主线, 在其二次规划(QP)子问题的求解中引入ADMM思想, 将QP分解为两个相互独立的小规模QP求解. 其次, 借助增广拉格朗日函数和Armijo线搜索产生原始变量新迭代点. 最后, 以显式解析式更新对偶变量. 因此, 构建了一个新型ADMM-SQP算法. 在较弱条件下, 分析了算法通常意义下的全局收敛性, 并对算法进行了初步的数值试验.     

二阶锥权互补问题的非精确非内点连续化算法

基于二阶锥权互补函数,将二阶锥权互补问题转化为一个方程组,运用非精确非内点连续化算法求解该方程组.该算法能以任意点作为初始点,且每次迭代时至多求解一个方程组.为节省算法求解方程组时的计算时间和内存,将非精确牛顿法引入到算法中.在适当假设下,证明了该算法是全局与局部二阶收敛的.最后数值实验表明了算法的良好性能.     

监督模糊模式识别交叉迭代模型

从模糊模式识别概念出发，建立一种以决策者经验、偏好为监督，在方案优属等级识别过程中确定最佳目标权重和方案优属度的监督模糊模式识别交叉迭代算法，该算法集成了决策偏好信息完全未知、部分未知、完全已知的主客观权重识别方法。并严格证明了该算法的局部收敛性。     

Distributed multi-agent optimization with state-dependent communication

We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. We study a projected multi-agent subgradient algorithm under state-dependent communication. The state-dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one. Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a “disagreement metric” between the agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this, we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence.     

Global Convergence of a Nonmonotone Trust Region Algorithm with Memory for Unconstrained Optimization

In this paper, we consider a trust region algorithm for unconstrained optimization problems. Unlike the traditional memoryless trust region methods, our trust region model includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. The numerical tests are also given to show the efficiency of our proposed method.     

凸约束优化问题的带记忆模型信赖域算法

本文我们考虑求解凸约束优化问题的信赖域方法 .与传统的方法不同 ,我们信赖域子问题的逼近模型中包括过去迭代点的信息 ,该模型使我们可以从更全局的角度来求得信赖域试探步 ,从而避免了传统信赖域方法中试探步的求取完全依赖于当前点的信息而过于局部化的困难 .全局收敛性的获得是依靠非单调技术来保证的     

有界约束半光滑方程组的非单调投影信赖域方法

投影信赖域策略结合非单调线搜索算法解有界约束非线性半光滑方程组.基于简单有界约束的非线性优化问题构建信赖域子问题,半光滑类牛顿步在可行域投影得到投影牛顿的试探步,获得新的搜索方向,结合非单调线搜索技术得到回代步,获得新的步长.在合理的条件下,证明算法不仅具有整体收敛性且保持超线性收敛速率.引入非单调技术能克服高度非线性的病态问题,加速收敛性进程,得到超线性收敛速率.     

装配型企业订货量分配与订单排产联合决策研究

针对供应商交货数量不确定环境下,多品种小批量装配型制造企业因生产物料不配套造成生产计划不可行甚至客户订单拖期的问题,从企业运作整体出发,考虑订货量分配决策对订单生产和交货的影响,以最小化采购成本和最小化订单排产相关成本为优化目标,在允许零部件拖期交货且供应商提供拖期价格折扣条件下,建立订货量分配与订单排产联合优化模型。针对可行解空间巨大、传统数学规划方法难以求解的问题,从增强搜索性能角度出发,设计基于自定义邻域搜索算子的局部搜索机制和基于随机与种群重构变异机制的改进粒子群算法的模型求解策略。通过应用实例对本文模型和算法进行了有效性验证和灵敏度分析,结果表明,相比于传统的分散决策方案,本文模型能够有效降低整体成本水平,引入的改进机制能够显著提升算法搜索性能,为企业供应风险下的运营决策制定提供理论参考。     

Approximate Greatest Descent Methods for Optimization with Equality Constraints

In an optimization problem with equality constraints the optimal value function divides the state space into two parts. At a point where the objective function is less than the optimal value, a good iteration must increase the value of the objective function. Thus, a good iteration must be a balance between increasing or decreasing the objective function and decreasing a constraint violation function. This implies that at a point where the constraint violation function is large, we should construct noninferior solutions relative to points in a local search region. By definition, an accessory function is a linear combination of the objective function and a constraint violation function. We show that a way to construct an acceptable iteration, at a point where the constraint violation function is large, is to minimize an accessory function. We develop a two-phases method. In Phase I some constraints may not be approximately satisfied or the current point is not close to the solution. Iterations are generated by minimizing an accessory function. Once all the constraints are approximately satisfied, the initial values of the Lagrange multipliers are defined. A test with a merit function is used to determine whether or not the current point and the Lagrange multipliers are both close to the optimal solution. If not, Phase I is continued. If otherwise, Phase II is activated and the Newton method is used to compute the optimal solution and fast convergence is achieved.     

Finding optimal memoryless policies of POMDPs under the expected average reward criterion

In this paper, partially observable Markov decision processes (POMDPs) with discrete state and action space under the average reward criterion are considered from a recent-developed sensitivity point of view. By analyzing the average-reward performance difference formula, we propose a policy iteration algorithm with step sizes to obtain an optimal or local optimal memoryless policy. This algorithm improves the policy along the same direction as the policy iteration does and suitable step sizes guarantee the convergence of the algorithm. Moreover, the algorithm can be used in Markov decision processes (MDPs) with correlated actions. Two numerical examples are provided to illustrate the applicability of the algorithm.     

求解箱式约束全局优化问题的新的F-C函数（英文）

To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a filled function and a cross function. The properties of the F-C function are discussed and the corresponding algorithm is given in this paper. F-C function has the same local minimizers with the objective function.Therefore, the F-C function method only needs to minimize the objective function once in the first iteration. Numerical experiments are performed and the results show that the proposed method is very effective.     

A Conic Trust-Region Method for Nonlinearly Constrained Optimization

Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.