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1.
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.  相似文献   

2.
In this paper,a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems.This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing Fisher-Burmeister function for the KKT first-order optimality conditions.Comparing with other QP-free methods, this method does not request the strict feasibility of iteration.In particular,this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points.Furthermore,the gradients of active constraints are not requested to be linearly independent.Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.  相似文献   

3.
本文利用一个新的分片线性NCP函数提出一个新的可行的QP-free方法解非线性不等式约束优化问题.不同于其他的QP-free方法,这个方法只考虑在工作集中的约束函数,工作集是积极集的一个估计,因此子问题的维数不是满秩的.这个方法可行的并且不需假定严格互补条件、聚点的孤立性得到算法的全局收敛性,并且积极约束函数的梯度不要求线性独立的,其中由拟牛顿法得到的子矩阵不需要求一致正定性.  相似文献   

4.
PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD   总被引:3,自引:0,他引:3  
In this paper,a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems.The new NCP functions are piece- wise linear-rational,regular pseudo-smooth and have nice properties.This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions,by using the piecewise NCP functions.This method is implementable and globally convergent without assuming the strict complementarity condition,the isolatedness of accumulation points.Fur- thermore,the gradients of active constraints are not requested to be linearly independent.The submatrix which may be obtained by quasi-Newton methods,is not requested to be uniformly positive definite.Preliminary numerical results indicate that this new QP-free method is quite promising.  相似文献   

5.
In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising.  相似文献   

6.
1. IntroductionConsider the optimization problemmin {f(x): gi(x) 5 0, j E I; x E R"}, (l)where f(x), gi(x): Rad - R, j E I ~ {1, 2,...,m}.It is well known that one of the most effective methods to solve problem (1) is thesequential quadratic programming (i.e., SoP) (see [1--6]), due to its property of superlinearconvergence. Especially in recent years, in order to perfect SoP both in theory and application, there have many papers, such as [7--10], been published. These papers focus mainly…  相似文献   

7.
In many mountainous areas, landslides and slope instabilities frequently occur after heavy rainfall and earthquake, and result in enormous casualties and huge economic losses. In order to mitigate the landslides hazard efficiently, a method is required for a better understanding of stability analysis. Fortunately, upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes. And in this approach, the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization. In general, the SQP-type algorithms are used to solve this optimization problem. However, it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the SQP-type algorithms. Fortunately, a QP-free algorithm based on penalty function and active-set strategy can be globally convergent toward the KKT points with arbitrary starting point, and the rate of convergence is local superlinear or even quadratic. Two classical problems of slope stability are solved by this QP-free algorithm. The results show that the QP-free algorithm would be the better choice than SQP-type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability.  相似文献   

8.
In this paper, we propose a feasible QP-free method for solving nonlinear inequality constrained optimization problems. A new working set is proposed to estimate the active set. Specially, to determine the working set, the new method makes use of the multiplier information from the previous iteration, eliminating the need to compute a multiplier function. At each iteration, two or three reduced symmetric systems of linear equations with a common coefficient matrix involving only constraints in the working set are solved, and when the iterate is sufficiently close to a KKT point, only two of them are involved. Moreover, the new algorithm is proved to be globally convergent to a KKT point under mild conditions. Without assuming the strict complementarity, the convergence rate is superlinear under a condition weaker than the strong second-order sufficiency condition. Numerical experiments illustrate the efficiency of the algorithm.  相似文献   

9.
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.  相似文献   

10.
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。  相似文献   

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