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．     

不等式约束优化一个具有超线性收敛的可行序列二次规划算法

建立了一个新的SQP算法,提出了一阶可行条件这一新概念．对已有SQP型算法进行改进,减少计算工作量,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

非线性最优化一个可行序列等式约束二次规划算法

本文针对非线性不等式约束优化问题,提出了一个新的可行序列等式约束二次规划算法．在每次迭代中,该算法只需求解三个相同规模且仅含等式约束的二次规划(必要时求解一个辅助的线性规划),因而其计算工作量较小．在一般的条件下,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

不等式约束优化一个新型可行QP-free算法

本文对非线性不等式约束优化问题提出了一个新的可行 QP-free 算法. 新算法保存了现有算法的优点, 并具有以下特性: (1) 算法每次迭代只需求解三个具有相同系数矩阵的线性方程组, 计算量小; (2) 可行下降方向只需通过求解一个线性方程组即可获得, 克服了以往分别求解两个线性方程组获得下降方向和可行方向, 然后再做凸组合的困难;(3) 迭代点均为可行点, 并不要求是严格内点; (4) 算法中采用了试探性线搜索,可以进一步减少计算量; (5) 算法中参数很少,数值试验表明算法具有较好的数值效果和较强的稳定性.     

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。     

非线性互补约束问题一个全局收敛的SQP算法

本文研究非线性互补约束优化问题,利用Fischer-Burmeister函数将非线性互补问题转化为非光滑方程,提出一个求解非线性互补约束问题的SQP算法,并在适当的假设下证明这个算法是全局收敛的.     

不等式约束优化一个超线性收敛的可行内点型算法

本文针对非线性不等式约束优化问题,提出了-个可行内点型算法.在每次迭代中,基于积极约束集策略,该算法只需求解三个线性方程组,因而其计算工作量较小.在-般的条件下,证明了算法具有全局收敛及超线性收敛性.     

非线性互补约束均衡问题的一个SQP算法

提出了一个求解非线性互补约束均衡问题(MPCC)的逐步逼近光滑SQP算法．通过一系列光滑优化来逼近MPCC．引入l1精确罚函数,线搜索保证算法具有全局收敛性．进而,在严格互补及二阶充分条件下,算法是超线性收敛的．此外,当算法有限步终止,当前迭代点即为MPEC的一个精确稳定点．     

不等式约束优化一个改进的投影变尺度算法

本文研究了不等式约束优化问题.利用共轭投影梯度方法,获得了一个投影变尺度型算法.在适当的条件下,证明算法是全局收敛且具有超线性收敛性.     

An improved SQP algorithm for inequality constrained optimization

In this paper, the feasible type SQP method is improved. A new algorithm is proposed to solve nonlinear inequality constrained problem, in which a new modified method is presented to decrease the computational complexity. It is required to solve only one QP subproblem with only a subset of the constraints estimated as active per single iteration. Moreover, a direction is generated to avoid the Maratos effect by solving a system of linear equations. The theoretical analysis shows that the algorithm has global and superlinear convergence under some suitable conditions. In the end, numerical experiments are given to show that the method in this paper is effective.This work is supported by the National Natural Science Foundation (No. 10261001) and Guangxi Science Foundation (No. 0236001 and 0249003) of China. Acknowledgement.We would like to thank one anonymous referee for his valuable comments and suggestions, which greatly improved the quality of this paper.     

An improved interior-type feasible QP-free algorithm for inequality constrained optimization problems

In this paper, an improved interior-type feasible QP-free algorithm for inequality constrained optimization problems is proposed. At each iteration, by solving three systems of linear equations with the same coefficient matrix, a search direction is generated. The algorithm is proved to be globally and superlinearly convergent under some mild conditions. Preliminary numerical results show that the proposed algorithm may be promising. Advantages of the algorithm include: the uniformly nonsingularity of the coefficient matrices without the strictly complementarity condition is obtained. Moreover, the global convergence is achieved even if the number of the stationary points is infinite.     

A type of efficient feasible SQP algorithms for inequality constrained optimization

In this paper, motivated by Zhu et al. methods [Z.B. Zhu, K.C. Zhang, J.B. Jian, An improved SQP algorithm for inequality constrained optimization, Math. Meth. Oper. Res. 58 (2003) 271-282; Zhibin Zhu, Jinbao Jian, An efficient feasible SQP algorithm for inequality constrained optimization, Nonlinear Anal. Real World Appl. 10(2) (2009) 1220-1228], we propose a type of efficient feasible SQP algorithms to solve nonlinear inequality constrained optimization problems. By solving only one QP subproblem with a subset of the constraints estimated as active, a class of revised feasible descent directions are generated per single iteration. These methods are implementable and globally convergent. We also prove that the algorithms have superlinear convergence rate under some mild conditions.     

不等式约束最优化超线性与二次收敛的强次可行SQP算法

利用ＳＱＰ方法、广义投影技术和强次可行方（向）法思想,建立不等式约束优化一个新的初始点任意的快速收敛算法． 算法每次迭代仅需解一个总存在可行解的二次子规划,或用广义投影计算“一阶”强次可行下降辅助搜索方向;采用曲线搜索与直线搜索相结合的方法产生步长． 在较温和的条件下,算法具有全局收敛性、强收敛性、超线性与二次收敛性． 给出了算法有效的数值试验．     

A cautious BFGS update for reduced Hessian SQP

In this paper, we introduce a cautious BFGS (CBFGS) update criterion in the reduced Hessian sequential quadratic programming (SQP) method. An attractive property of this update criterion is that the generated iterative matrices are always positive definite. Under mild conditions, we get the global convergence of the reduced Hessian SQP method. In particular, the second order sufficient condition is not necessary for the global convergence of the method. Furthermore, we show that if the second order sufficient condition holds at an accumulation point, then the reduced Hessian SQP method with CBFGS update reduces to the reduced Hessian SQP method with ordinary BFGS update. Consequently, the local behavior of the proposed method is the same as the reduced Hessian SQP method with BFGS update. The presented preliminary numerical experiments show the good performance of the method. This work was supported by the National Natural Science Foundation of China via grant 10671060 and 10471060.     

A TRUST—REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION

This paper presents a new trust-region algorithm for n-dimension nonlinear optimiza-tion subject to m nonlinear inequality constraints.Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm.Global convergence of the algorithun to a first-order KKT point is eatablished under mild conditions on the trial steps.local quadratic convergence theorem is provcd for nondegenerate minimizer point.Numerical expcriment is prcsented to show the effectiveness of our approach.     

An SQP-filter method for inequality constrained optimization and its global convergence

In this paper, we combine the filter technique with a modified sequential quadratic programming (SQP) method. The optimization solution is obtained by reducing step length, which is obtained by an exact linear search. Furthermore, this method can start with an infeasible initial point. The method uses a filter to promote global convergence.