求解二次规划逆问题的非单调信赖域算法

为了提高求解二次规划逆问题的速度,提出了针对求解该问题的非单调信赖域算法.为了降低问题的复杂度,将二次规划逆问题转换为决策变量相对较少的对偶问题,采用增广Lagrange法构造对偶问题的子问题,并通过引入光滑函数将子问题转换为无约束优化问题,利用非单调信赖域算法进行求解.数值实验结果表明,该算法的迭代次数比牛顿算法、Gauss回代交替方向法少,运行速度快.因此,对于大规模二次规划逆问题,该算法更加有效.     

基于信赖域Newton 算法的ELM网络

针对极端学习机(ELM)网络伪逆输出权值计算方法的运算复杂度制约其训练速度问题,提出一种基于信赖域Newton算法的新型ELM网络(TRON-ELM),并采用信赖域Newton算法求解ELM网络的输出权值.该算法首先构造一个ELM网络代价函数的Newton方程,并将其作为一个无约束优化问题,采用共轭梯度法求解,避免了求代价函数Hessian矩阵逆的运算,提高了训练速度,信赖域条件的存在保证了算法的整体收敛性.仿真实验结果验证了所提出方法的有效性.     

基于信赖域二次规划的非线性模型预测控制优化算法

针对非线性预测控制如何在有限时域内有效的求解非凸非线性规划这一关键问题, 本文采用序列二次规划方法, 将非线性规划转化为一系列二次子规划求解. 首先根据非线性规划联立方法将系统状态和控制量同时作为优化变量, 得到以控制量步长为优化变量, 只包含不等式约束的子二次规划问题, 并用它取代原SQP子规划, 减小了子问题的规模; 随后采用基于信赖域二次规划的方法求解子规划问题, 保证每次迭代的可行性; 同时采用一种能够保持SQP问题Hessian矩阵稀疏结构的更新方法, 也在一定程度上降低了算法的复杂程度.最后的仿真结果表明了该方法的有效性.     

一种求解半定规划的非单调信赖域算法

提出一种求解半定规划的非单调信赖域算法。利用推广至矩阵域的光滑Fischer-Burmeister函数,转化半定规划的最优性条件,改写半定规划的中心路径,得到与其等价的无约束优化问题的非线性可微光滑方程组,在求解信赖域子问题时,利用当前迭代点的一阶梯度信息,给出信赖域半径的选取机制。仿真结果表明,与经典的内点算法相比,对于一般规模(n, m≤30)的半定规划问题,该算法的运行速度较快。对于大规模的半定规划问题(n, m＞30),该算法更适合处理Norm min、Lovasz这2类问题。     

求解二维Fredholm积分方程的参数化信赖域方法

给出了求解二维第一类Fredholm积分方程信赖域方法。通过引入正则化参数将离散后的Fredholm积分方程转化带参数的最优化问题,借助于KKT条件将二次信赖域子问题参数化,并进行分析求解,最后给出了数值模拟。     

用改进的信赖域方法求解二次插值模型

一种改进的信赖域方法被用来解无约束最优化问题,当目标函数的导数信息不可利用或者求解目标函数的导数代价太大。通常,考虑用二次插值模型来逼近目标函数,并且用传统的信赖域方法求解这个二次模型。传统的信赖域方法将被改进,并且形成两个改进的信赖域子问题。改进的信赖域方法的创新点在于:求解二次模型在一个参数化的信赖域中,修改这个模型在另一个参数化的信赖域当中。在这两个新的信赖域中,可以分别很快地找到一个好的下降方向和一个具有均衡性的插值点。这个改进的方法不但节省了函数值计算次数而且提高了解的精度。实验结果表明,针对测试问题,提出的方法的确是优于传统的信赖域方法的。     

求解半定规划的新算法

为了提高求解半定规划问题的运算效率,提出了一种新的求解半定规划的非单调信赖域算法。将半定规划的最优性条件转化为无约束优化问题,并构造无约束优化问题的信赖域子问题,修正信赖域半径的校正条件,当初始搜索点处于峡谷附近时仍能搜索到全局最优解。实验结果表明,对于小规模和中等规模的半定规划问题,该算法的迭代次数都比经典的内点算法少,运行速度快。     

求解半定规划的新算法

为了提高求解半定规划问题的运算效率,提出了一种新的求解半定规划的非单调信赖域算法。将半定规划的最优性条件转化为无约束优化问题,并构造无约束优化问题的信赖域子问题,修正信赖域半径的校正条件,当初始搜索点处于峡谷附近时仍能搜索到全局最优解。实验结果表明,对于小规模和中等规模的半定规划问题,该算法的迭代次数都比经典的内点算法少,运行速度快。     

非单调信赖域方法求解无约束非光滑优化问题

提出了非单调信赖域算法求解无约束非光滑优化问题,并和经典的信赖域方法作比较分析。同时,设定了一些条件,在这些假设条件下证明了该算法是整体收敛的。数值实验结果表明,非单调策略对无约束非光滑优化问题的求解是行之有效的,拓展了非单调信赖域算法的应用领域。     

一种求解无约束优化问题的非单调信赖域算法

提出了非单调信赖域算法求解基于锥模型的无约束优化问题,该算法在求解信赖域子问题时充分利用了当前迭代点的一阶梯度信息。提出了一个新的信赖域半径的选取机制,并和经典的信赖域方法作比较分析。设定了一些条件,在这些假设条件下证明了算法是整体收敛的。数值实验结果表明,该算法对基于锥模型的无约束优化问题的求解是行之有效的,拓展了非单调信赖域算法的应用领域。     

解离散系数滤波器设计问题的分支定界算法

基于离散系数滤波器设计问题已有的半定规划松弛模型,利用文献[6]的方法给出了该问题的二次规划松弛模型,该模型能给出比半定规划模型更好的界,然后运用分支定界方法求解该模型。与随机扰动方法相比,该方法能得到一个性能更好的次优解,对于精度要求较高的滤波器设计问题,这种方法非常有效,并通过了仿真实验的证实。     

Embedded MPC Controller Based on Interior‐Point Method with Convergence Depth Control

To allow the implementation of model predictive control on the chip, we first propose a primal–dual interior point method with convergence depth control to solve the quadratic programming problem of model predictive control. Compared with algorithms based on traditional termination criterion, the proposed method can significantly reduce the computation cost while obtaining an approximate solution of the quadratic programming problem with acceptable optimality and precision. Thereafter, an embedded model predictive controller based on the quadratic programming solver is designed and implemented on a digital signal processor chip and a prototype system is built on a TMDSEVM6678LE digital signal processor chip. The controller is verified on two models by using the hardware in loop frame to mimic real applications. The comparison shows that the whole design is competitive in real‐time applications. The typical computation time for quadratic programming problems with 5 decision variables and 110 constraints can be reduced to less than 2 ms on an embedded platform.     

General redundancy optimization method for cooperating manipulatorsusing quadratic inequality constraints

In redundancy optimization problems related to cooperating manipulators such as optimal force distribution, constraints on the physical limits of the manipulators should be considered. We propose quadratic inequality constraints (QICs), which lead to ellipsoidal feasible regions, to solve the optimization problem more efficiently. We investigate the effect of the use of QICs from the points of view of problem size and change of the feasible region. To efficiently deal with the QICs, we also propose the dual quadratically constrained quadratic programming (QCQP) method. In this method, the size of the optimization problem is reduced so that the computational burden is lightened. The proposed method and another well-known quadratic programming method are applied to the two PUMA robots system and compared with each other. The results show that the use of QICs with the dual QCQP method allows for faster computation than the existing method     

Monotone Smoothing Splines using General Linear Systems

In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by the second‐order integrator, but not for other cases. The difficulty in the problem is that the monotonicity constraint should be satisfied over an interval which has the cardinality of the continuum. To solve this problem, we first formulate the problem as a semi‐infinite quadratic programming problem, and then we adopt a discretization technique to obtain a finite‐dimensional quadratic programming problem. It is shown that the solution of the finite‐dimensional problem always satisfies the infinite‐dimensional monotonicity constraint. It is also proved that the approximated solution converges to the exact solution as the discretization grid‐size tends to zero. An example is presented to show the effectiveness of the proposed method.     

基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem

This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature.     

求解互补支持向量机的非单调信赖域算法

求解支持向量机的核心问题是对一个大规模凸二次规划问题进行求解。基于支持向量机的修正模型,得到一个与之等价的互补问题,利用Fischer-Burmeister互补函数,从一个新的角度提出了求解互补支持向量机的非单调信赖域算法。新算法避免了求解Hesse矩阵或矩阵求逆运算,减少了工作量,提高了运算效率。在不需要任何假设的情况下,证明算法具有全局收敛性。数值实验结果表明,对于大规模非线性分类问题,该算法的运行速度比LSVM算法和下降法快,为求解SVM优化问题提供了一种新的可行方法。     

A dual Newton strategy for tree‐sparse quadratic programs and its implementation in the open‐source software treeQP

This paper presents a dual Newton scheme for tree‐sparse quadratic programs as they may arise in the field of stochastic programming. Previous work suggests to introduce auxiliary variables to decompose the tree into scenarios and use Newton's method to solve a dual problem formulation. Following a different approach, we apply the same principle directly on the tree‐sparse problem, avoiding the increase in dimensionality. In combination with a tailored algorithm for the calculation of the step direction, which is typically the most expensive operation per iteration, the proposed algorithm achieves a linear complexity in the number of nodes and supports parallel processing of the tree branches in a stage‐wise fashion. An open‐source implementation of the presented dual Newton strategy is publicly available in treeQP , a toolbox of open‐source solvers for tree‐sparse quadratic programs.     

分布式整数规划及其在航线扰动问题的应用

在航空公司的运作中时常会出现干扰它正常运作的现象。在这种情况下,航空公司必须马上制定航线修复计划使受到干扰的航线尽快复原,以防止更大面积的航班取消和航班延误。提出一种基于递增映射迭代方法的分布式整数规划算法来解决由于机场关闭引起的航线扰动问题。整个问题分成了两个子问题：可行航线的生成和飞机的重指派。第一个子问题的问题空间被初始点分割方法分割成了若干片段。然后在一个分布式的计算网络中使用递增映射迭代方法在分得的每个片段上同时求解第一个子问题。得到的可行航线用来求解第二个子问题。最后的算例结果可以发现提出的方法要好于CPLEX和多目标基因算法。     

量子粒子群优化算法在训练支持向量机中的应用

训练支持向量机的本质问题就是求解二次规划问题，但对大规模的训练样本来说，求解二次规划问题困难很大。遗传算法和粒子群算法等智能搜索技术可以在较少的时间开销内给出问题的近似解。量子粒子群优化（QPSO）算法是在经典的微粒群算法的基础上所提出的一种有较高收敛性和稳定性的进化算法。将操作简单而收敛快速的QPSO算法运用于训练支持向量机，优化求解二次规划问题．为解决大规模的二次规划问题开辟了一条新的途径。