二维黎曼流形的Voronoi图生成算法

提出采用黎曼流形描述研究对象和基于坐标卡生成Voronoi图的算法思路.讨论了黎曼流形上研究Voronoi图的难点,并给出了存在定理,该定理说明了坐标卡上Voronoi图的存在条件.按照算法思路和存在定理,详细描述了二维黎曼流形上创建坐标卡的算法,并给出流形上转换函数和混合函数的定义方法.最后描述了基于坐标卡生成Voronoi图的算法,并给出了具体实例.     

Lagrange神经网络的稳定性分析

若重新定义与不等式约束相关的乘子为正定函数,则在构造Lagrange神经网络时,可直接使用处理等式约束的方法处理不等式约束,不需再用松驰变量将不等式约束转换为等式约束,减小了网络实现的复杂程度.利用Liapunov一阶近似原理,严格分析了这类Lagrange神经网络的局部稳定性;并采用LaSalle不变集原理,讨论其大范围稳定性.     

有等式约束优化问题的粒子群优化算法

目前大多数粒子群优化算法针对无约束优化问题或不等式约束优化问题，求解有等式约束优化问题的方法是把每个等式约束变成两个不等式约束，这种方法的缺点是在进化过程中粒子位置很难满足等式约束条件，影响了收敛速度和解的精度。提出了求解有等式约束优化问题的两种新粒子群优化算法，数值试验结果表明，算法是有效的。     

时变不确定切换广义系统的鲁棒最优保性能控制

针对一类时变参数不确定切换广义系统,对其鲁棒最优保性能控制问题进行研究,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件。通过构造广义Lyapunov函数和线性矩阵不等式方法,给出系统鲁棒最优保性能控制器存在的充分条件。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到鲁棒最优保性能控制律及闭环性能指标上界。最后用示例说明该方法的有效性。     

不确定广义时滞系统的鲁棒稳定方法研究

研究一类带有时滞不确定广义系统的鲁棒渐近稳定问题．利用Lyapunov稳定性定理和线性矩阵不等式工具，得到了广义系统正则、鲁棒渐近稳定的时滞相关充分条件．为了降低所得结果的保守性，避免了采用系统模型变换和利用矩阵不等式方法．进一步，建立一个具有线性矩阵不等式约束的凸优化问题，利用Matlab软件中的LMI工具箱求解，得到保证广义系统鲁棒渐近稳定的最大可允许时滞上界．仿真示例表明了该方法的有效性．     

求解约束优化问题的协同进化教与学优化算法

对约束优化问题,为了避免罚因子和等式约束转化为不等式约束时引入的约束容忍度参数所带来的不便,本文在基本教与学优化（Teaching-learning-based optimization,TLBO）算法中加入了自我学习过程并提出了一种求解约束优化问题的协同进化教与学优化算法,使得罚因子和约束容忍度随种群的进化动态调整.对7个常见测试函数的数值实验验证了算法求解带有等式和不等式约束优化问题的有效性.     

一种单交叉路口的信号混合优化方法

针对包含不等式约束和等式约束的城市单交叉路口信号优化问题,为缓解交通堵塞和安全性,设计了一种混合优化方法.方法首先采用自适应惩罚策略,将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题;然后再分别采用自适应实数编码遗传算法和一种变搜索空间局部搜索算法进行混合优化,为了提高实数编码遗传算法的优化效果,设计了一种自适应交叉概率和变异概率.最后针对多种交通需求模式,应用混合优化方法进行了大量的仿真计算,结果表明在城市单交叉路口信号优化问题中具有良好的优化效果.     

自适应惩罚策略及其在交通信号优化中的应用

针对约束优化问题的求解,设计了一种处理约束条件的自适应惩罚策略,用于将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题。该策略通过引入约束可行测度、可行度的概念来描述决策变量服从于不等式约束和等式约束的程度,并以此构造处理约束条件的自适应惩罚函数,惩罚值随着约束可行度的变化而动态自适应地改变。为了检验该惩罚策略的有效性,针对单路口交通信号优化问题进行了应用研究,并用三种不同算法进行了大量的仿真计算,结果表明所设计的自适应策略在具有高度约束条件的城市交通信号优化问题中具有良好的效果。     

广义区间系统的稳定性与二次能稳分析

对于一类广义区间系统,利用Lyapunov方法,研究了该系统的稳定性.通过广义Lyapunov不等式的建立,得到了此系统结构稳定的充分必要条件是广义Lyapunov不等式有解.在此基础上,建立了广义Riccati不等式,由此不等式得到了此系统二次能稳的充要条件是广义Riccati不等式有解.这些结果将对进一步研究此系统有着重要的基础作用.最后,举例说明了主要结果.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

On the existence of solutions to a class of optimization problems

A sufficient condition for the existence and uniqueness of solutions to a class of optimization problems in nonlinear programming form, with strictly convex cost functions, convex inequality and linear equality side constraints, and closed convex constraint sets is studied.     

Entropy Optimization Models with Convex Constraints

In this paper, we study the minimum cross-entropy optimization problem subject to a general class of convex constraints. Using a simple geometric inequality and the conjugate inequality we demonstrate how to directly construct a "partial" geometric dual program which allows us to apply the dual perturbation method to derive the strong duality theorem and a dual-to-primal conversion formula. This approach generalizes the previous results of linearly, quadratically, and entropically constrained cross-entropy optimization problems and provides a platform for using general purpose optimizers to generate ε-optimal solution pair to the problem.     

Control Liapunov function design of neural networks that solve convex optimization and variational inequality problems

This paper presents two neural networks to find the optimal point in convex optimization problems and variational inequality problems, respectively. The domain of the functions that define the problems is a convex set, which is determined by convex inequality constraints and affine equality constraints. The neural networks are based on gradient descent and exact penalization and the convergence analysis is based on a control Liapunov function analysis, since the dynamical system corresponding to each neural network may be viewed as a so-called variable structure closed loop control system.     

Quasi-Lagrangian Neural Network for Convex Quadratic Optimization

A new neural network for convex quadratic optimization is presented in this brief. The proposed network can handle both equality and inequality constraints, as well as bound constraints on the optimization variables. It is based on the Lagrangian approach, but exploits a partial dual method in order to keep the number of variables at minimum. The dynamic evolution is globally convergent and the steady-state solutions satisfy the necessary and sufficient conditions of optimality. The circuit implementation is simpler with respect to existing solutions for the same class of problems. The validity of the proposed approach is verified through some simulation examples.     

基于逻辑"或"约束优化的实时系统设计

标准约束优化问题的等式或不等式约束之间是逻辑"与"关系,目前已经有很多高效、收敛的优化算法.但是,在实际应用中有很多更一般的约束优化问题,其等式或不等式约束之间不仅包含逻辑"与"关系,而且还包含逻辑"或"关系,现有的针对标准约束优化问题的各种算法不再适用.给出一种新的数学变换方法,把具有逻辑"或"关系的不等式约束转换为一组具有逻辑"与"关系的不等式,并应用到实时单调速率调度算法的可调度性判定充要条件中,把实时系统设计表示成混合布尔型整数规划问题,利用经典的分支定界法求解.实验部分指出了各种方法的优缺点.     

A computational method for parameter optimization problems arising in control†

A parameter optimization procedure is presented for large-scale problems arising in linear control system design that include equality and inequality constraints. The procedure is based on a novel min—max algorithm for locating a constrained relative minimum without the use of penalty functions or slack variables. This algorithm is constructed from an auxiliary minimization problem with equality constraints. Inequality constraints then are introduced using the notion of an effective constraint. Typical problem formulations are discussed, and an extensive design example is presented.     

A new gradient-based neural network for solving linear andquadratic programming problems

A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality constraints are properly handled. The simulation results show that the proposed neural network is feasible and efficient.     

An interior penalty method for inequality constrained optimal control problems

This paper presents a penalty function approach to the solution of inequality constrained optimal control problems. The method begins with a point interior to the constraint set and approaches the optimum from within, by solving a sequence of problems with only terminal conditions as constraints. Thus, all intermediate solutions satisfy the inequality constraints. Conditions are given which guarantee that the un "constrained" problems have solutions interior to the constraint set and that in the limit these solutions converge to the constrained optimum. For linear systems with convex objective and concave inequalities, the unconstrained problems have the property that any local minimum is global. Further, under these conditions, upper and lower bounds in the optimum are easily available. Three test problems are solved and the results presented.     

Parameter constraints in generalized linear latent variable models

Parameter constraints in generalized linear latent variable models are discussed. Both linear equality and inequality constraints are considered. Maximum likelihood estimators for the parameters of the constrained model and corrected standard errors are derived. A significant reduction in the dimension of the optimization problem is achieved with the proposed methodology for fitting models subject to linear equality constraints.     

Using augmented Lagrangian particle swarm optimization for constrained problems in engineering">Using augmented Lagrangian particle swarm optimization for constrained problems in engineering

The comparatively new stochastic method of particle swarm optimization (PSO) has been applied to engineering problems especially of nonlinear, non-differentiable, or non-convex type. Its robustness and its simple applicability without the need for cumbersome derivative calculations make PSO an attractive optimization method. However, engineering optimization tasks often consist of problem immanent equality and inequality constraints which are usually included by inadequate penalty functions when using stochastic algorithms. The simple structure of basic particle swarm optimization characterized by only a few lines of computer code allows an efficient implementation of a more sophisticated treatment of such constraints. In this paper, we present an approach which utilizes the simple structure of the basic PSO technique and combines it with an extended non-stationary penalty function approach, called augmented Lagrange multiplier method, for constraint handling where ill conditioning is a far less harmful problem and the correct solution can be obtained even for finite penalty factors. We describe the basic PSO algorithm and the resulting method for constrained problems as well as the results from benchmark tests. An example of a stiffness optimization of an industrial hexapod robot with parallel kinematics concludes this paper and shows the applicability of the proposed augmented Lagrange particle swarm optimization to engineering problems.