带等式约束二次规划子问题的滤子SQP算法

一类求解非线性规划问题的滤子序列二次规划(SQP)方法被提出.为了提高收敛速度,给目标函数和约束违反度函数都设置了斜边界.二次规划子问题(QP)设置为两项:不等式约束QP和等式约束QP.两个子问题产生的搜索方向进行线性迭加后为算法的搜索方向.这样的设置可以改善收敛性,并调节算法运行中的一些不良效果.在较温和的条件下,可得到全局收敛性.     

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.     

基于积极集识别技术的半无限minimax问题非单调有限记忆SQP算法

本文研究了半无限minimax问题.利用积极集识别技术结合非单调有限记忆序列二次规划(SQP)方法来求解半无限minimax问题.在适当的条件下证明了算法的收敛性.数值结果表明新算法在降低求解规模和迭代次数等方面均优于采用Armijo型线搜索的SQP方法.     

半无限规划离散化问题一个两阶段序列二次规划算法

本文研究了求解半无限规划离散化问题(P)的一个新的算法.利用序列二次规划(SQP)两阶段方法和约束指标集的修正技术,提出了求解(P)的一个两阶段SQP算法.算法结构简单,搜索方向的计算成本较低.在适当的条件下,证明了算法具有全局收敛性.数值试验结果表明算法是有效的.推广了文献[4]中求解(P)的算法.     

一类随机非线性规划的积极集SQP算法

在等价非线性扩展模型的基础上,给出了求解一类随机非线性规划的序列二次规划(sequential quadratic programming,简称SQP)算法.与标准SQP算法不同,本文算法采用积极集方法求解SQP子问题以加快收敛速度,并采用滤子方法确定搜索步长,克服了传统方法选取惩罚因子的困难.在一定条件下证明了所给算法的收敛性.最后,通过一个数值例子验证了该方法的有效性.     

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．     

一个改进的SQP型算法

本文建立非线性等式和不等式约束规划问题的一个序列二次规划(SQP)型算法.算法的每次迭代只需解一个确实可解的二次规划，然后对其解进行简单的显式校正，便可产生关于罚函数是下降的搜索方向，克服Maratos效应.在适当的假设条件下，还论证了算法的全局收敛性和超级收敛性.     

基于并行计算的多方向强次可行模松弛SQP算法

本文研究求解非线性约束优化问题.利用多方向并行方法,提出了一个新的强次可行模松弛序列二次规划(SQP)算法.数值试验表明,迭代次数和计算时间少于只取单一参数的传统算法.     

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.     

一种基于LVI求解二次规划问题的数值算法

给出并研究了一种数值算法(简称94LVI算法),用于求解带等式和双端约束的二次规划问题. 这类带约束的二次规划问题首先被转换为线性变分不等式问题,该问题等价于分段线性投影等式.接着使用94LVI算法求解上述分段线性投影等式,从而得到QP问题的最优解. 进一步给出了94LVI算法的全局收敛性证明. 94LVI算法与经典有效集算法的对比实验结果证实了给出的94LVI算法在求解二次规划问题上的高效性与优越性.     

A feasible filter SQP algorithm with global and local convergence

A feasible sequential quadratic programming (SQP) filter algorithm is proposed for general nonlinear programming. It is based on the modified quadratic programming (QP) subproblem in which each iteration proceeds in two phases. The first phase solves a general convex QP problem which does not require any feasibility restoration phase whose computation may be expensive. And, under some mild conditions, the global convergence is proved. The second phase can make the presented SQP method derive quadratic convergence by employing exact Hessian information.     

A New Nonmonotone Linesearch SQP Algorithm for Unconstrained Minimax Problem

In this article, unconstrained minimax problems are discussed, and a sequential quadratic programming (SQP) algorithm with a new nonmonotone linesearch is presented. At each iteration, a search direction of descent is obtained by solving a quadratic programming (QP). To circumvent the Maratos effect, a high-order correction direction is achieved by solving another QP and a new nonmonotone linesearch is performed. Under reasonable conditions, the global convergence and the rate of superlinear convergence are established. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

An improved sequential quadratic programming algorithm for solving general nonlinear programming problems

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of the sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising.     

Feasible generalized monotone line search SQP algorithm for nonlinear minimax problems with inequality constraints

In this paper, the nonlinear minimax problems with inequality constraints are discussed, and a sequential quadratic programming (SQP) algorithm with a generalized monotone line search is presented. At each iteration, a feasible direction of descent is obtained by solving a quadratic programming (QP). To avoid the Maratos effect, a high order correction direction is achieved by solving another QP. As a result, the proposed algorithm has global and superlinear convergence. Especially, the global convergence is obtained under a weak Mangasarian–Fromovitz constraint qualification (MFCQ) instead of the linearly independent constraint qualification (LICQ). At last, its numerical effectiveness is demonstrated with test examples.     

A ROBUST SQP METHOD FOR OPTIMIZATION WITH INEQUALITY CONSTRAINTS

A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.     

Global convergence on an active set SQP for inequality constrained optimization

Sequential quadratic programming (SQP) has been one of the most important methods for solving nonlinearly constrained optimization problems. In this paper, we present and study an active set SQP algorithm for inequality constrained optimization. The active set technique is introduced which results in the size reduction of quadratic programming (QP) subproblems. The algorithm is proved to be globally convergent. Thus, the results show that the global convergence of SQP is still guaranteed by deleting some “redundant” constraints.     

A kind of nonmonotone filter method for nonlinear complementarity problem

The nonlinear complementarity problem can be reformulated as a nonlinear programming. For solving nonlinear programming, sequential quadratic programming (SQP) type method is very effective. But the QP subproblem may be inconsistent. In this paper, we propose a kind nonmonotone filter method in which the QP subproblem is consistent. By means of nonmonotone filter, this method has no demand on the penalty parameter which is difficult to obtain. Moreover, the restoration phase is not needed any more. Under reasonable conditions, we obtain the global convergence of the algorithm. Some numerical results are presented.     

解非线性规划问题的不精确线性搜索SQP滤子方法

本文用序列二次规划方法(SQP)结合Wolfe-Powell不精确线性搜索准则求解非线性规划问题.Wolfe-Powell准则是一种能够使目标函数获得充分下降而运行时间较省的确定步长方法.不精确线性搜索滤子方法比较其它结合精确线性搜索和信赖域方法求解问题的滤子方法更灵活更易实现.如果目标函数的预测下降量为负,我们的工作将主要利用可行恢复项改善可行性.一般条件下,本文提出的算法较易实现,且具有全局收敛性.数值试验显示了算法的有效性.     

Sparse quadratic programming in chemical process optimization

The quadratic programming aspects of a full space successive quadratic programming (SQP) method are described. In particular, fill-in, matrix factor and active set updating, numerical stability, and indefiniteness of the Hessian matrix are discussed in conjunction with a sparse modification of Bunch and Parlett factorization of symmetric indefinite (Kuhn-Tucker) matrices of the type often encountered in optimization. A new pivoting strategy, called constrained pivoting, is proposed to reduce fill-in and compared with complete, partial and threshold pivoting. It is shown that constrained pivoting often significantly reduces fill-in and thus the iterative computational burdens associated with the factorization and solution of Kuhn-Tucker conditions within the QP subproblem. A numerical algorithm for updating the lower triangular and diagonal factors is presented and shown to be very fast, usually requiring only about 5% of the cost of refactorization. Two active set strategies are also presented. These include the options of adding inequalities either one or several at a time. In either case, the effects on matrix factor updating is shown to be small. Finally, a simple test is used to maintain iterative descent directions in the quadratic program. Our sparse symmetric indefinite QP algorithm is tested in the context of a family of SQP algorithms that include a full space Newton method with analytical derivatives, a full space BFGS method and a Range and Null space Decomposition (RND) method in which the projected Hessian is calculated from either analytical second derivatives or the BFGS update. Several chemical process optimization problems, with small and large degrees of freedom, are used as test problems. These include minimum work calculations for multistage isothermal compression, minimum area targeting for heat exchanger networks, and distillation optimizations involving some azeotropic and extractive distillations. Numerical results show uniformly that both the proposed QP and SQP algorithms, particularly the full space Newton method, are reliable and efficient. No failures were experienced at either level.