一般约束优化基于识别函数的模松弛算法

借助于半罚函数和产生工作集的识别函数以及模松弛SQP算法思想, 本文建立了求解带等式及不等式约束优化的一个新算法. 每次迭代中, 算法的搜索方向由一个简化的二次规划子问题及一个简化的线性方程组产生. 算法在不包含严格互补性的温和条件下具有全局收敛性和超线性收敛性. 最后给出了算法初步的数值试验报告.     

一个等式约束问题的SQP方法及其收敛性

本文提出一个SQP算法,其效益函数为Flether^[1]提出的连续可微精确罚函数。该算法具有全局收敛性和超线性收敛速度,并且能自动调节罚参数,能有效地处理计算搜索方向的二次子规划的不可行问题。     

一种修正的线搜索Filter-SQP算法

序列二次规划(SQP)算法是解非线性优化问题最有效的方法之一,然而当QP子问题不相容时SQP算法将会失败,且在罚函数中选择合适的罚参数比较困难.此处在原Filter-SQP算法的基础上,利用特定的凸规划模型代替QP子问题,提出一种修正的线搜索filter-SQP算法,并证明它的全局收敛性.此算法原理简单,容易实现,且具有全局收敛性,数值实验表明它是有效的.     

不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

针对带不等式约束的极大极小问题,借鉴一般约束优化问题的模松弛强次可行SQP算法思想,提出了求解不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法.首先,通过在QCQP子问题中选取合适的罚函数,保证了算法的可行性以及目标函数F(x)的下降性,同时简化QCQP子问题二次约束项参数α_k的选取,可保证算法的可行性和收敛性.其次,算法步长的选取合理简单.最后,在适当的假设条件下证明了算法具有全局收敛性及强收敛性.初步的数值试验结果表明算法是可行有效的.     

一类新的罚函数与罚算法(英)

在本文中,我们提出了带不等式约束的非线性规划问题的一类新的罚函数,它的一个子类可以光滑逼近$l_1$罚函数. 基于此类新的罚函数我们给出了一种罚算法,这个算法的特点是每次迭代求出罚函数的全局精确解或非精确解. 在很弱的条件下算法总是可行的. 我们在不需要任何约束规范的情况下,证明了算法的全局收敛性. 最后给出了数值实验.     

非线性互补约束均衡问题的一个滤子SQP算法

提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的.     

化不等式约束问题为无约束的广义可微限域精确罚函数方法

本文给出了广义可微精确罚函数的概念及一类所谓广义限域可微精确罚函数.本文预先选定罚因子,将不等式约束问题化为单一的无约束问题,并给出了具全局收敛性的算法.本文的罚函数构造简单,假设条件少而且算法的构造与收敛性结果是独特的.     

一类修改的带NCP函数信赖域滤子算法

本文针对非线性规划给出了一种修改的带NCP函数的信赖域滤子SQP算法,主要的修改之处是用NCP函数替代了滤子中约束违反度函数,而且进一步证明了这种修改的算法同样具有全局收敛性.     

求解一般约束优化问题的一个全局收敛的混合不精确SQP算法

对于一般约束优化问题,本文通过一种特殊的耦合策略,把一个局邵超线性收敛的不精确SQP算法与广义梯度投影法相结合,从而给出了一个混合算法.该算法无需计算拉格朗日函数的海色矩阵,并且在适当的假设下,算法具有全局和局部超线性收敛性.     

不等式约束优化问题的低阶精确罚函数的光滑化算法

对不等式约束优化问题提出了一个低阶精确罚函数的光滑化算法. 首先给出了光滑罚问题、非光滑罚问题及原问题的目标函数值之间的误差估计,进而在弱的假
设之下证明了光滑罚问题的全局最优解是原问题的近似全局最优解. 最后给出了一个基于光滑罚函数的求解原问题的算法,证明了算法的收敛性,并给出数值算例说明算法的可行性.     

General Information

In this paper, a new sequential penalty algorithm, based on the L_infin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm.     

A new constraint test-case generator and the importance of hybrid optimizers

In the past decade, significant progress has been made in understanding problem complexity of discrete constraint problems. In contrast, little similar work has been done for constraint problems in the continuous domain. In this paper, we study the complexity of typical methods for non-linear constraint problems and present hybrid solvers with improved performance. To facilitate the empirical study, we propose a new test-case generator for generating non-linear constraint satisfaction problems (CSPs) and constrained optimization problems (COPs). The optimization methods tested include a sequential quadratic programming (SQP) method, a penalty method with a fixed penalty function, a penalty method with a sequence of penalty functions, and an augmented Lagrangian method. For hybrid solvers, we focus on the form that combines two or more optimization methods in sequence. In the experiments, we apply these methods to solve a series of continuous constraint problems with increasing constraint-to-variable ratios. The test problems include artificial benchmark problems from the test-case generator and problems derived from controlling a hyper-redundant modular manipulator. We obtain novel results on complexity phase transition phenomena of the various methods. Specifically, for constraint satisfaction problems, the SQP method is the best on weakly constrained problems, whereas the augmented Lagrangian method is the best on highly constrained ones. Although the static penalty method performs poorly by itself, by combining it with the SQP method, we show a hybrid solver that is significantly better than any of the individual methods on problems with moderate to large constraint-to-variable ratios. For constrained optimization problems, the hybrid solver obtains much better solutions than SQP, while spending comparable amount of time. In addition, the hybrid solver is flexible and can achieve good results on time-bounded applications by setting parameters according to the time limits.     

一个修正的SQP方法-滤子方法

序列二次规划方法（SQP）是解决非线性规划问题最有效的算法之一，但是当QP子问题不可行时算法可能会失败．而且线搜索中的罚参数的选择通常比较困难．在文献[1]中，SQP方法得到了修正，使得QP子问题可行．在本文中，我们利用滤子技术避免了罚函数的使用同时提出了带线搜索的滤子方法，最终保证了SQP方法总是可行的，而且得到了方法的全局收敛性．     

Г-环的单位元与其算子环的单位元之间的关系

г—环的单位元是其算子环中的元素.本文探讨Г—的单位与其算子环的单位元之间的关系.举例表明存在Г—环(Г_N—环)M,它的左、右算子环均有单位元,而M既无左单位元,又无右单位元.那么在什么条件下,Г—环(Г_N—环)的左、右算子环具有单位元时,其本身必定具有左、右单位元呢?对Г—环和Г_N—环分别探讨了此问题,并给出了了解答此问题的充要条件.     

A robust SQP method based on a smoothing lower order penalty function†

Based on a smoothing approximation of a lower order penalty function and following Facchinei's method of dealing with the inconsistency of subproblems in SQP methods, we present a new robust SQP algorithm for solving a nonlinear constrained optimization problem. The proposed algorithm incorporates automatic adjustment rules for the choice of parameters. Under a new regularity condition at infeasible points, the algorithm is proved to be globally convergent.     

Penalty functions,Newton's method,and quadratic programming

In this paper, the search directions computed by two versions of the sequential quadratic programming (SQP) algorithm are compared with that computed by attempting to minimize a quadratic penalty function by Newton's method, and it is shown that the differences are attributable to ignoring certain terms in the equation for the Newton correction. Since the effect of ignoring these terms may be to make the resultant direction a poor descent direction for the quadratic penalty function, it is argued that the latter is an inappropriate merit function for use with SQP. A method is then suggested by which these terms may be included without losing the benefits gained from the use of the orthogonal transformations derived from the constraints Jacobian.The authors wish to thank A. R. Conn and N. I. M. Gould for spirited discussions which took place when the second author spent some time at Waterloo, Ontario, Canada; they also thank L. C. W. Dixon for the clarifications that he suggested to the penultimate draft of this paper.     

On the convergence of a new trust region algorithm

Summary. In this paper we present a new trust region algorithm for general nonlinear constrained optimization problems. The algorithm is based on the exact penalty function. Under very mild conditions, global convergence results for the algorithm are given. Local convergence properties are also studied. It is shown that the penalty parameter generated by the algorithm will be eventually not less than the norm of the Lagrange multipliers at the accumulation point. It is proved that the method is equivalent to the sequential quadratic programming method for all large , hence superlinearly convergent results of the SQP method can be applied. Numerical results are also reported. Received March 21, 1993     

等式约束优化一个新的SQP算法

提出了一个处理等式约束优化问题新的SQP算法,该算法通过求解一个增广Lagrange函数的拟Newton方法推导出一个等式约束二次规划子问题,从而获得下降方向．罚因子具有自动调节性,并能避免趋于无穷．为克服Maratos效应采用增广Lagrange函数作为效益函数并结合二阶步校正方法．在适当的条件下,证明算法是全局收敛的,并且具有超线性收敛速度．     

A Modified SQP Method with Nonmonotone Linesearch Technique

In this paper, a modified SQP method with nonmonotone line search technique is presented based on the modified quadratic subproblem proposed in Zhou (1997) and the nonmonotone line search technique. This algorithm starts from an arbitrary initial point, adjusts penalty parameter automatically and can overcome the Maratos effect. What is more, the subproblem is feasible at each iterate point. The global and local superlinear convergence properties are obtained under certain conditions.