非线性不等式约束最优化一个超线性与二次收敛的强次可行方法

本文讨论非线性不等式约束最优化问题，借助于序列线性方程组技术和强次可行方法思想，建立了问题的一个初始点任意的快速收敛新算法．在每次迭代中，算法只需解一个结构简单的线性方程组．算法的初始迭代点不仅可以是任意的，而且不使用罚函数和罚参数，在迭代过程中，迭代点列的可行性单调不减．在相对弱的假设下，算法具有较好的收敛性和收敛速度，即具有整体与强收敛性，超线性与二次收敛性．文中最后给出一些数值试验结果．     

非线性最优化一个超线收敛的可行下降算法

本文讨论非线性等式和不等式约束最优化的求解方法。首先将原问题扩充成一个只含不等式约束的参数规划，对于充分大的参数，扩充问题与原问题是等价的。然手建立具有以下特点的一个新算法。１）算法对扩充问题而言是可行下降的，参数只须自动调整有限次；２）每次迭代仅需解一个二次规划；３）在适当的假设下，算法超线性收敛于原问题的最优解。     

一类线性约束下不可微最优化问题的可行下降方法

本文给出了一类线性约束下不可微量优化问题的可行下降方法，这类问题的目标函数是凸函数和可微函数的合成函数，算法通过解系列二次规划寻找可行下降方向，新的迭代点由不精确线搜索产生，在较弱的条件下，我们证明了算法的全局收敛性     

非线性不等式约束最优化快速收敛的可行信赖域算法

In this paper,by combining the trust region technique with the generalized gradient projection.a new trust region algorithm with feasible iteration points is presented for nonlinear inequality constrained optimization,and its trust region is a general compact set containing the origion as an inteior point.No penalty function is used in the algorithm,and it is feasible descent .Under suitable assumptions,the algorithm is proved to possess global and strong convergence as well as superlinear and quadratic convergence.Some numerical results are reported.     

超线性与二次收敛的序列方程组可行方法

本文讨论不等式约束规划问题,给出一个线性方程组与辅助方向相结合的新可行算法,算法用一种新型的直线搜索产生步长.在一定条件下,当k充分大后,求方向dk每次只需解一个线性方程组.文中证明了算法的全局收敛性与超线性的收敛速度以及二次收敛性,并给出了方法初步的数值试验.     

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．     

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.     

非线性约束条件下一个超线性收敛的可行方法

在本文中，我们对非线性不等式约束条件下的非线性优化问题给出了一个新的ＳＱＰ类可行方法．此算法不但结构简单、易于计算，并且在适当的假设条件下，我们证明了算法具有全局收敛性及超线性收敛性     

超线性与二次收敛序列线性方程组算法

本文,在无严格互补条件下,对非线性不等式约束最优化问题提出了一个新的序列线性方程组(简称SSLE)算法．算法有两个重要特征:首先,每次迭代,只须求解一个线性方程组或一个广义梯度投影阵,且线性方程组可以无解．其次,初始点可以任意选取．在无严格互补条件下,算法仍有全局收敛性、强收敛性、超线性收敛性及二次收敛性．文章的最后,还对算法进行了初步的数值实验．     

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．     

A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization

Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising.     

Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization

A new, infeasible QP-free algorithm for nonlinear constrained optimization problems is proposed. The algorithm is based on a continuously differentiable exact penalty function and on active-set strategy. After a finite number of iterations, the algorithm requires only the solution of two linear systems at each iteration. We prove that the algorithm is globally convergent toward the KKT points and that, if the second-order sufficiency condition and the strict complementarity condition hold, then the rate of convergence is superlinear or even quadratic. Moreover, we incorporate two automatic adjustment rules for the choice of the penalty parameter and make use of an approximated direction as derivative of the merit function so that only first-order derivatives of the objective and constraint functions are used.     

A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems

In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.     

Globally Convergent Inexact Quasi-Newton Methods for Solving Nonlinear Systems

Large scale nonlinear systems of equations can be solved by means of inexact quasi-Newton methods. A global convergence theory is introduced that guarantees that, under reasonable assumptions, the algorithmic sequence converges to a solution of the problem. Under additional standard assumptions, superlinear convergence is preserved.     

Superlinearly Convergent Trust-Region Method without the Assumption of Positive-Definite Hessian

In this paper, we reinvestigate the trust-region method by reformulating its subproblem: the trust-region radius is guided by gradient information at the current iteration and is self-adaptively adjusted. A trust-region algorithm based on the proposed subproblem is proved to be globally convergent. Moreover, the superlinear convergence of the new algorithm is shown without the condition that the Hessian of the objective function at the solution be positive definite. Preliminary numerical results indicate that the performance of the new method is notable. The authors thank the Associate Editor and two anonymous referees for valuable comments and suggestions. This work was supported by the National Science Foundation of China, Grant 70302003. Communicated by T. Rapcsak     

不等式约束最优化的一个使用非单调搜索的可行算法

对不等式约束最优化问题本文提出了一个新算法。算法使用了非单调搜索,它不仅放松了每步迭代中对搜索的限制,而且使得算法迭代到一定阶段后具有非常简洁的形式,在不需要严格互补条件的较弱假设下,算法是整体和超线性收敛的。     

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported. Project supported by the National Natural Science Foundation (No. 10261001), Guangxi Science Foundation (Nos. 0236001, 064001), and Guangxi University Key Program for Science and Technology Research (No. 2005ZD02) of China.     

一类优化问题的快速收敛算法

给出了一个用于解决 LC1线性约束优化问题的 BFGS-SQP算法 ,这个算法是用 Armijo线性原则来求步长的 .为推广 BFGS-SGP算法 ,本文采用 Wolfe线性搜索原则来替代该 BFGS-SQP算法的 Armijo原则 ,经过分析 ,同样得到了 BFGS-SGP算法的全局收敛性及超线性收敛性