In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is ...In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.展开更多
In this paper,we present a successive quadratic programming(SQP)method for minimizing a class of nonsmooth functions,which are the sum of a convex function and a nonsmooth composite function.The method generates new i...In this paper,we present a successive quadratic programming(SQP)method for minimizing a class of nonsmooth functions,which are the sum of a convex function and a nonsmooth composite function.The method generates new iterations by using the Armijo-type line search technique after having found the search directions.Global convergence property is established under mild assumptions.Numerical results are also offered.展开更多
In this paper, a modified variation of the Limited SQP method is presented for constrained optimization. This method possesses not only the information of gradient but also the information of function value. Moreover,...In this paper, a modified variation of the Limited SQP method is presented for constrained optimization. This method possesses not only the information of gradient but also the information of function value. Moreover, the proposed method requires no more function or derivative evaluations and hardly more storage or arithmetic operations. Under suitable conditions, the global convergence is established.展开更多
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...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.展开更多
A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possibl...A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.展开更多
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the m...A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.展开更多
In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an ...In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an exact penalty function as the merit function to determine if the trial step is accepted.The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an-stationary point is analyzed.We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition.Numerical results demonstrate that,compared to the state-of-the-art algorithms,SQP-PG is an effective method for equality constrained composite optimization problems.展开更多
基金Supported by the National Natural Science Foundation of China(1 9971 0 0 2 )
文摘In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity.
文摘In this paper,we present a successive quadratic programming(SQP)method for minimizing a class of nonsmooth functions,which are the sum of a convex function and a nonsmooth composite function.The method generates new iterations by using the Armijo-type line search technique after having found the search directions.Global convergence property is established under mild assumptions.Numerical results are also offered.
文摘In this paper, a modified variation of the Limited SQP method is presented for constrained optimization. This method possesses not only the information of gradient but also the information of function value. Moreover, the proposed method requires no more function or derivative evaluations and hardly more storage or arithmetic operations. Under suitable conditions, the global convergence is established.
基金This work is supported in part by the National Natural Science Foundation of China (Grant No. 10171055).
文摘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.
基金This research is supportedin part by the National Natural Science Foundation ofChina(Grant No. 39830070).
文摘A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.
基金Supported by the National Natural Sciences Foundation of China (No.39830070 and 10171055).
文摘In this paper, a new SQP method for inequality constrained optimization is proposed and the global convergence is obtained under very mild conditions.
基金This research is supported in part by the National Natural Science Foundation of China(No. 39830070).
文摘In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
基金Supported by the National Natural Science Foundation of China(1 980 1 0 0 9) and by the Natural Sci-ence Foundation of Guangxi
文摘A new SQP type feasible method for inequality constrained optimization is presented,it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations.The directions of the master algorithm are generated by only one quadratic programming, and its step\|size is always one, the directions of the auxiliary algorithm are new “second\|order” feasible descent. Under suitable assumptions,the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence.
基金supported by the National Natural Science Foundation of China(Grant No.72394365).
文摘In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an exact penalty function as the merit function to determine if the trial step is accepted.The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an-stationary point is analyzed.We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition.Numerical results demonstrate that,compared to the state-of-the-art algorithms,SQP-PG is an effective method for equality constrained composite optimization problems.
基金The National Natural Science Foundation of China(11271086)he Natural Science Foundation of Guangxi Province(2011GXNSFD018022)he Innovation Group of Talents Highland of Guangxi Higher School
