基于线性约束规划问题的神经网络模型

提出了一种基于梯度投影矩阵下的求解线性约束下规划问题的神经网络模型，并导出了线性约束下规划问题的稳定解法，该网络模型既适合于求解线性约束下线性或非二次规划问题，又适合于求解线性或非线性方程组，与其它规划问题的神经网络相比，更具有一般性。     

一种线性约束规划问题的神经网络模型及其应用

提出了一种基于梯度投影矩阵下的求解线性约束下规划问题的神经网络。针对解的稳定性问题,导出了该网络相关参数之间的关系。由文中定义可知,该网络不但适合于求解线性约束下线性或非二次规划问题,而且也用于求解线性或非线性方程组问题,比其它规划问题的神经网络方法更具有一般性。     

等式约束凸二次规划解析的新型神经网络方法*

针对不同于传统基于梯度法的递归神经网络定义一种基于标量范数取值的非负能量函数,通过定义一种基于向量取值的不定无界的误差函数,构建了一种能实时求解具有线性等式约束的凸二次规划问题。基于Simulink仿真平台的计算机实验结果表明,该新型神经网络模型能够准确有效地求解此类二次规划问题。     

面向冗余度机械臂QP问题求解的E47和94LVI数值算法

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束,且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求。考虑同时受制于上述三种约束的二次规划问题的求解,给出并研究两种数值算法(E47和94LVI算法)。这类带约束的二次规划问题被等价转换为分段线性投影方程。应用E47和94LVI算法求解上述分段线性投影方程,从而得到二次规划问题的最优数值解。同时,通过大量的数值实验,研究两种算法面向冗余度机械臂的QP问题求解性能,并给出E47、94LVI算法与经典有效集算法的对比实验结果。最终证实了E47和94LVI两种算法在求解二次规划问题上的高效性和优越性。     

面向冗余度机械臂QP问题求解的E47和94LⅥ数值算法

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束,且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求.考虑同时受制于上述三种约束的二次规划问题的求解,给出并研究两种数值算法(E47和94LⅥ算法).这类带约束的二次规划问题被等价转换为分段线性投影方程.应用E47和94LⅥ算法求解上述分段线性投影方程,从而得到二次规划问题的最优数值解.同时,通过大量的数值实验,研究两种算法面向冗余度机械臂的QP问题求解性能,并给出E47、94LⅥ算法与经典有效集算法的对比实验结果.最终证实了E47和94LⅥ两种算法在求解二次规划问题上的高效性和优越性.     

Lagrange双支撑向量回归机

提出一种快速的支撑向量回归算法。首先将支撑向量回归的带有两组约束的二次规划问题转化为两个小的分别带有一组约束的二次规划问题,而每一个小的二次规划问题又采用一种快速迭代算法求解,该迭代算法能从任何初始点快速收敛,避免了二次优化问题求解,因此能显著提高训练速度。在多个标准数据集上的实验表明,该算法比传统支撑向量机快很多,同时具有良好的泛化性能。     

基于Oracle罚方法的混合约束差分进化算法

为有效求解复杂约束优化问题,提出了一种基于Oracle的混合约束差分进化算法OBHSaDE.在OBHSaDE算法中,首先对Oracle罚方法进行了改进,并符合约束优化问题的求解要求.利用改进后的Oracle罚方法来快速找到问题的可行域,借助无约束优化算法SaDE能对可行域进行有效搜索,利用序列二次规划的超线性的收敛速度来减少评估次数和提高解的质量.仿真结果表明,改进算法不仅减少了评估次数、提高了解的质量,且具有很好的鲁棒性,还具有较少的用户参数,提高了算法的实用性.OBHSaDE是求解约束优化问题的一种具有竞争力的新方法.     

改进粒子群算法在支持向量机训练中的应用

训练支持向量机需要求解二次规划问题,LPSO算法对于求解含线性约束优化问题是一种直观、简单的方法。改进后的LPSO算法较好的解决了早熟收敛问题。对谷氨酸发酵过程建模的实验表明本文提出的方法训练精度高,泛化能力强。     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

一类特殊凸二次双层规划的算法

根据值型凸二次双层规划的Johri对偶理论,讨论一类特殊双层规划——上层仅含一个不等式约束的非减值型线性．凸二次双层规划的办法,通过把对其Johri对偶规划的求解转化为对有限个凸二次规划的求解,给出求解该类双层规划的一种多项式时间算法。     

一种求解线性约束的非线性规划神经网络方法

针对线性约束的非线性规划的求解问题,利用罚函数求解优化问题的思想将其转化为二次凸规划,基于神经网络的结构特性,定义所需的能量函数,从而使网络收敛于唯一稳定点最终实现线性约束的非线性规划的求解。实验仿真结果表明,该方法是有效和正确的,且能推广到含参的非线性规划和多目标规划中去。     

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.     

Solving the stochastic support vector regression with probabilistic constraints by a high-performance neural network model

This paper offers a recurrent neural network to support vector machine (SVM) learning in stochastic support vector regression with probabilistic constraints. The SVM is first converted into an equivalent quadratic programming (QP) formulation in linear and nonlinear cases. An artificial neural network for SVM learning is then proposed. The presented neural network framework guarantees obtaining the optimal solution of the SVM problem. The existence and convergence of the trajectories of the network are studied. The Lyapunov stability for the considered neural network is also shown. The efficiency of the proposed method is shown by three illustrative examples.

     

基于约束区域神经网络的动态遗传算法

提出一种基于约束区域神经网络的动态遗传算法,将遗传算法的全局搜索和约束区域神经网络模型的局部搜索结合了起来.利用动态遗传算法确定神经网络模型的初始点,同时使用神经网络确定动态遗传算法的适应度函数.该算法具有一定的理论意义和生物意义.与标准的遗传算法相比,缩小了搜索规模,可获得不定二次规划问题更好的近似最优解.     

Neural network approach for allocation with capacity

In this paper we discuss neural network approach for allocation with capacity constraints problem. This problem can be formulated as zero-one integer programming problem. We transform this zero-one integer programming problem into an equivalent nonlinear programming problem by replacing zero-one constraints with quadratic concave equality constraints. We propose two kinds of neural network structures based on penalty function method and augmented Lagrangian multiplier method, and compare them by theoretical analysis and numerical simulation. We show that penalty function based neural network approach is not good to combinatorial optimization problem because it falls in the dilemma whether terminating at an infeasible solution or sticking at any feasible solution, and augmented Lagrangian multiplier method based neural network can alleviate this suffering in some degree.     

A high-performance neural network for solving linear and quadraticprogramming problems

Two classes of high-performance neural networks for solving linear and quadratic programming problems are given. We prove that the new system converges globally to the solutions of the linear and quadratic programming problems. In a neural network, network parameters are usually not specified. The proposed models can overcome numerical difficulty caused by neural networks with network parameters and obtain desired approximate solutions of the linear and quadratic programming problems.     

Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems.

Most existing neural networks for solving linear variational inequalities (LVIs) with the mapping Mx + p require positive definiteness (or positive semidefiniteness) of M. In this correspondence, it is revealed that this condition is sufficient but not necessary for an LVI being strictly monotone (or monotone) on its constrained set where equality constraints are present. Then, it is proposed to reformulate monotone LVIs with equality constraints into LVIs with inequality constraints only, which are then possible to be solved by using some existing neural networks. General projection neural networks are designed in this correspondence for solving the transformed LVIs. Compared with existing neural networks, the designed neural networks feature lower model complexity. Moreover, the neural networks are guaranteed to be globally convergent to solutions of the LVI under the condition that the linear mapping Mx + p is monotone on the constrained set. Because quadratic and linear programming problems are special cases of LVI in terms of solutions, the designed neural networks can solve them efficiently as well. In addition, it is discovered that the designed neural network in a specific case turns out to be the primal-dual network for solving quadratic or linear programming problems. The effectiveness of the neural networks is illustrated by several numerical examples.     

A New Optimal Force Distribution Scheme of Multiple Cooperating Robots Using Dual Method

A new optimal force distribution scheme of multiple cooperating robots is proposed, in which the duality theory of nonlinear programming (NLP) is combined with the quadratic programming (QP) approach. The optimal force distribution problem is formulated as a QP problem with both linear and quadratic constraints, and its solution is obtained by an efficient algorithm. The use of the quadratic constraints is important in that it considerably reduces the number of constraints, thus enabling the Dual method of NLP to be used in the solution algorithm. Moreover, it can treat norm constraints without approximation, such as bound of the norm of the force exerted by each robot. The proposed scheme is more efficient in terms of speed than any other method. Numerical examples of two PUMA robot task using the proposed method and a well-known fast method are compared, and the results indicate the capability of real time application of our method.     

Predictive control based on neural network models with I/O feedback linearization

This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, while allowing only for a small performance degradation.     

A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming.

In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.