无约束极小化的子空间迭代法

一、引 言 最优化方法中的无约束极小化问题,除了有其本身的重要性以外,还经常作为一个约束最优化问题的子问题出现.但很多处理具有非线性约束的最优化问题的方法常造成病态的无约束子问题,也就是说需要极小化的函数在极值点附近Hesse矩阵的条件很坏,接近于奇异.例如在罚函数方法(Penalty function methods)中,要极小化一系列辅助函数     

线性–非二次最优控制问题的一种解法

讨论了求解状态终端无约束线性–非二次最优控制问题的拟Riccati方程方法, 并据此提出了计算无约束线性–非二次问题之数值解的方法; 然后将这个方法与一种能近似地化有约束问题为无约束问题的惩罚方法结合起来, 给出了一种算法, 可以计算状态终端有约束的线性–非二次最优控制问题之近似解.     

足球机器人挑球机构优化设计

为优化足球机器人挑球机构的关键参数,根据所建的机构数学模型,在Matlab中采用SUMT惩罚函数法,通过构造增广目标函数,把约束最优化问题转换为一系列无约束极小化问题,获得原约束问题的最优解,对模型进行优化.软件仿真与实物实验表明,将该结果应用到足球机器人设计中,使机器人挑球性能大大提高,验证模型的正确性,并为足球机器人在挑球过程中球与带球机构碰撞问题提供参考性解决方案.     

基于求解大规模界约束问题的三种有效集识别策略的比较

针对大规模界约束优化问题,列举了四种有效集识别策略,每次迭代它们允许多个有效约束的指标加到工作集或从工作集中去掉.在1998年Facchinei等人提出的有效集算法[4]基础上,写出有效集拟牛顿算法(ASNA)框架用于测试不同的有效集识别策略.采用特殊的方法,由非线性无约束问题产生若干界约束极小化的测试问题,通过数值测试发现Facchinei等人同年提出的精确有效集识别函数[5]不适用于本文的ASNA算法,最终分析了其余三种识别策略的优缺点.     

线性多变量系统设计自由度利用的探讨

本文提出一种参数最优化的方法,对状态反馈阵最小范数问题和最优极点配置问题进行了探讨。前者归结为平方和形式函数无约束极小化问题,后者归结为多元多项式函数无约束极小化问题。     

平滑支持向量机聚类研究

支持向量聚类（Suppoa Vector Clustering,SVC）的运算有较高的计算复杂性,本文在优化过程中引入惩罚函数,以此作为目标函数的惩罚项,并用一个平滑函数来近似正号函数,并将优化问题的不等式约束消去,得到一个无约束问题。再利用BFGS—Annijo算法来求解该无约束问题。理论和仿真结果表明该方法提高优化问题的求解效率。     

带不等式路径约束最优控制问题的惩罚函数法

控制变量参数化（Control variable parameterization,CVP）方法是目前求解流程工业中最优操作问题的主流数值方法,但如果问题中包含路径约束,特别是不等式路径约束时,CVP方法则需要考虑专门的处理手段.为了克服该缺点,本文提出一种基于L1精确惩罚函数的方法,能够有效处理关于控制变量、状态变量、甚至控制变量/状态变量复杂耦合形式下的不等式路径约束.此外,为了能使用基于梯度的成熟优化算法,本文还引进了最新出现的光滑化技巧对非光滑的惩罚项进行磨光.最终得到了能高效处理不等式路径约束的改进型CVP架构,并给出相应数值算法.经典的带不等式路径约束最优控制问题上的测试结果及与国外文献报道的比较研究表明:本文所提出的改进型CVP 架构及相应算法在精度和效率上兼有良好表现.     

改进的Mumford-Shah模型及其基于逐段常数水平集方法在图像处理中的应用

为了快速的分割和去噪, 经典的 Mumford-Shah 模型需要增强惩罚项的作用, 即增大惩罚项系数, 但是将使目标逐渐的消失. 本文工作提出一个改进的 Mumford-Shah 模型避免了如此现象, 并结合逐段常数水平集方法和梯度下降法求解极小化问题. 并用仿真实验证明了新模型和运算的有效性.     

一类整数性目标规划的遗传算法

本文给出了以惩罚函数法将约束优化问题转化为无约束优化问题的通用算法,提出了将遗传算法和惩罚函数法相结合用于求解整数性目标规划问题的具体方法。计算机数值仿真结果表明了该方法的有效性。     

训练支持向量机的Huber近似算法

支持向量机是基于统计学习理论的结构风险最小化原理提出来的一种新的学习算法,它把模式识别问题建模为一个简单约束的高维二次规划问题．该文利用Lagrangian对偶方法,给出此高维二次规划的无约束对偶问题;考虑到该对偶问题是不可微的,利用Huber近似将其近似转化为连续可微的分片二次函数的无约束极小化问题．证明了该分片二次函数的极小点对应原二次规划的ε最优解,而用此极小点可直接算出支持向量和最优超平面．最后针对分片二次函数的特点,提出了Newton型算法,结合精确一维搜索技巧,可以快速求解该问题．数据实验结果仿真表明该算法能够在低存储需求下有效提高大数据量、高维问题的训练学习速度．     

A BFGS-SQP method for nonsmooth,nonconvex, constrained optimization and its evaluation using relative minimization profiles

We propose an algorithm for solving nonsmooth, nonconvex, constrained optimization problems as well as a new set of visualization tools for comparing the performance of optimization algorithms. Our algorithm is a sequential quadratic optimization method that employs Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton Hessian approximations and an exact penalty function whose parameter is controlled using a steering strategy. While our method has no convergence guarantees, we have found it to perform very well in practice on challenging test problems in controller design involving both locally Lipschitz and non-locally-Lipschitz objective and constraint functions with constraints that are typically active at local minimizers. In order to empirically validate and compare our method with available alternatives—on a new test set of 200 problems of varying sizes—we employ new visualization tools which we call relative minimization profiles. Such profiles are designed to simultaneously assess the relative performance of several algorithms with respect to objective quality, feasibility, and speed of progress, highlighting the trade-offs between these measures when comparing algorithm performance.     

A globally and quadratically convergent algorithm for general nonlinear programming problems

This paper presents an algorithm for the minimization of a nonlinear objective function subject to nonlinear inequality and equality constraints. The proposed method has the two distinguishing properties that, under weak assumptions, it converges to a Kuhn-Tucker point for the problem and under somewhat stronger assumptions, the rate of convergence is quadratic. The method is similar to a recent method proposed by Rosen in that it begins by using a penalty function approach to generate a point in a neighborhood of the optimum and then switches to Robinson's method. The new method has two new features not shared by Rosen's method. First, a correct choice of penalty function parameters is constructed automatically, thus guaranteeing global convergence to a stationary point. Second, the linearly constrained subproblems solved by the Robinson method normally contain linear inequality constraints while for the method presented here, only linear equality constraints are required. That is, in a certain sense, the new method “knows” which of the linear inequality constraints will be active in the subproblems. The subproblems may thus be solved in an especially efficient manner. Preliminary computational results are presented.     

Filter design subject to nonlinear side constraints

Preliminary results show sequential unconstrained minimization techniques (SUMT) to be a viable filter design method. A nonlinear optimal filter design problem subject to nonlinear side constraints is formulated and solved using SUMT.     

A dual formulation for generating information about constrained optima in automated design

Certain properties of geometric programming are used to develop a method for generating information about the optimum design for problems involving the minimization of a real valued function subject to inequality constraints. This information includes a lower bound on the global minimum value of the merit function, details of which constraints are active at the optimum and values of the characteristics associated with non-active constraints. An active set strategy is then presented to obtain the optimum design without invoking a formal search procedure. Approximations will usually be required for the merit function and constraints, and accuracy and convergence are considered. Application of these methods to problems associated with the minimum weight design of aerospace structures is demonstrated.     

基于拉格朗日对偶结合粒子群优化的无线Mesh网络信道分配方案

本文提出了一种拉格朗日对偶结合粒子群优化的信道分配方案。该算法能使用WMN中所有可用信道（非重叠和部分重叠信道）进行信道分配,根据路径转发权重来设定信道分配顺序,从而提高网络的吞吐量。同时,综合考虑信道间隔和节点之间的距离来衡量干扰影响,使节点可以选择具有较少干扰的信道。最终得到原始WMN优化问题的最优解,实现最大化网络吞吐量和最小化网络干扰。实验结果表明,相比其他几种现有的无线mesh网络信道分配方案,提出的方案具有更好的性能。     

A globally convergent algorithm for minimizing over the rotationgroup of quadratic forms

The authors describe a numerical procedure for solving problems involving minimization over the rotation group of quadratic forms which arise in connection with problems of computer vision. The algorithm presented is a sequential quadratic programming method which takes advantage of the special structure of the problem constraints. It is demonstrate that the method is globally convergent     

Stability and approximation of maximin problems

For maximin problems with bound constraints we show that the soft set theory approach lets us significantly weaken stability conditions and approximation conditions for such problems with the method of penalty functions.     

Using a modified genetic algorithm to minimize the production costs for slabs of precast prestressed concrete joists

Genetic algorithms (GAs) are search methods that have been successfully applied to a variety of tasks. This paper describes the use of a modified GA as an optimization method in structural engineering for minimizing the production costs of slabs using precast prestressed concrete joists. The work initially identifies and describes the multiple costs involved in the production of these slabs and then combines them into a function subjected to 28 equality and inequality constraints. The experiments conducted address the minimization of this function using GA, where constraints are treated using a penalty technique. In addition, results obtained with a conventional optimization method are presented, for comparison.     

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.     

基于PAC-Bayes边界理论的SVM模型选择方法

PAC-Bayes边界理论融合了贝叶斯定理和随机分类器的结构风险最小化原理,它作为一个理论框架,能有效评价机器学习算法的泛化性能。针对支持向量机（SVM）模型选择问题,通过分析PAC-Bayes边界理论框架及其在SVM上的应用,将PAC-Bayes边界理论与基于交叉验证的网格搜索法相结合,提出一种基于PAC-Bayes边界的SVM模型选择方法（PBB-GS）,实现快速优选SVM的惩罚系数和核函数参数。UCI数据集的实验结果表明该方法优选出的参数能使SVM具有较高的泛化性能,并具有简便快速、参数选择准确的优点,能有效改善SVM模型选择问题。