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1.
JIANJINBAO 《高校应用数学学报(英文版)》1997,12(3):343-354
In this paper, a new superlinearly convergent algorithm is presented for optimization problems with general nonlineer equality and inequality Constraints, Comparing with other methods for these problems, the algorithm has two main advantages. First, it doesn‘t solve anyquadratic programming (QP), and its search directions are determined by the generalized projection technique and the solutions of two systems of linear equations. Second, the sequential points generated by the algoritbh satisfy all inequity constraints and its step-length is computed by the straight line search,The algorithm is proved to possesa global and auperlinear convergence. 相似文献
2.
Jin-bao Jian Qing-jie Hu Chun-ming Tang Hai-yan Zheng 《Applied Mathematics and Optimization》2007,56(3):343-363
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. 相似文献
3.
An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point 总被引:6,自引:0,他引:6
For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search
direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this
algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related
quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using ε-active set procedure
with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general
nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems
of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence.
To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.
Project partly supported by the National Natural Science Foundation of China and Tianyuan Foundation of China. 相似文献
4.
J. B. Jian 《Journal of Optimization Theory and Applications》2006,129(1):109-130
This paper discusses optimization problems with nonlinear inequality constraints and presents a new sequential quadratically-constrained
quadratic programming (NSQCQP) method of feasible directions for solving such problems. At each iteration. the NSQCQP method
solves only one subproblem which consists of a convex quadratic objective function, convex quadratic equality constraints,
as well as a perturbation variable and yields a feasible direction of descent (improved direction). The following results
on the NSQCQP are obtained: the subproblem solved at each iteration is feasible and solvable: the NSQCQP is globally convergent
under the Mangasarian-Fromovitz constraint qualification (MFCQ); the improved direction can avoid the Maratos effect without
the assumption of strict complementarity; the NSQCQP is superlinearly and quasiquadratically convergent under some weak assumptions
without thestrict complementarity assumption and the linear independence constraint qualification (LICQ).
Research supported by the National Natural Science Foundation of China Project 10261001 and Guangxi Science Foundation Projects
0236001 and 0249003.
The author thanks two anonymous referees for valuable comments and suggestions on the original version of this paper. 相似文献
5.
One of the most interesting topics related to sequential quadratic programming algorithms is how to guarantee the consistence
of all quadratic programming subproblems. In this decade, much work trying to change the form of constraints to obtain the
consistence of the subproblems has been done. The method proposed by De O. Pantoja J.F. A. and coworkers solves the consistent
problem of SQP method, and is the best to the authors’ knowledge. However, the scale and complexity of the subproblems in
De O. Pantoja’s work will be increased greatly since all equality constraints have to be changed into absolute form. A new
sequential quadratic programming type algorithm is presented by means of a special ε-active set scheme and a special penalty
function. Subproblems of the new algorithm are all consistent, and the form of constraints of the subproblems is as simple
as one of the general SQP type algorithms. It can be proved that the new method keeps global convergence and Local superlinear
convergence.
Project partly supported by the National Natural Science Foundation of China. 相似文献
6.
This paper discusses a special class of mathematical programs with nonlinear complementarity constraints, its goal is to present a globally and superlinearly convergent algorithm for the discussed problems. We first reformulate the complementarity constraints as a standard nonlinear equality and inequality constraints by making use of a class of generalized smoothing complementarity functions, then present a new SQP algorithm for the discussed problems. At each iteration, with the help of a pivoting operation, a master search direction is yielded by solving a quadratic program, and a correction search direction for avoiding the Maratos effect is generated by an explicit formula. Under suitable assumptions, without the strict complementarity on the upper-level inequality constraints, the proposed algorithm converges globally to a B-stationary point of the problems, and its convergence rate is superlinear.AMS Subject Classification: 90C, 49MThis work was supported by the National Natural Science Foundation (10261001) and the Guangxi Province Science Foundation (0236001, 0249003) of China. 相似文献
7.
LiPingZHANG JiYeHAN ZhengHaiHUANG 《数学学报(英文版)》2005,21(1):117-128
We propose a one-step smoothing Newton method for solving the non-linear complementarity problem with P0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function(for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0-NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions. 相似文献
8.
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. 相似文献
9.
10.
An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions. 相似文献
11.
We present a globally convergent phase I-phase II algorithm for inequality-constrained minimization, which computes search directions by approximating the solution to a generalized quadratic program. In phase II these search directions are feasible descent directions. The algorithm is shown to converge linearly under convexity assumptions. Both theory and numerical experiments suggest that it generally converges faster than the Polak-Trahan-Mayne method of centers.The research reported herein was sponsored in part by the Air Force Office of Scientific Research (Grant AFOSR-90-0068), the National Science Foundation (Grant ECS-8713334), and a Howard Hughes Doctoral Fellowship (Hughes Aircraft Co.). 相似文献
12.
Jin-bao Jian Ran Quan Qing-jie Hu 《应用数学学报(英文版)》2007,23(3):395-410
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. 相似文献
13.
The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results. 相似文献
14.
Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions 总被引:1,自引:0,他引:1
Jin-Bao Jian Chun-Ming Tang Hai-Yan Zheng 《European Journal of Operational Research》2010,200(3):645-657
In this paper, we present a sequential quadratically constrained quadratic programming (SQCQP) norm-relaxed algorithm of strongly sub-feasible directions for the solution of inequality constrained optimization problems. By introducing a new unified line search and making use of the idea of strongly sub-feasible direction method, the proposed algorithm can well combine the phase of finding a feasible point (by finite iterations) and the phase of a feasible descent norm-relaxed SQCQP algorithm. Moreover, the former phase can preserve the “sub-feasibility” of the current iteration, and control the increase of the objective function. At each iteration, only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction. Without any other correctional directions, the global, superlinear and a certain quadratic convergence (which is between 1-step and 2-step quadratic convergence) properties are proved under reasonable assumptions. Finally, some preliminary numerical results show that the proposed algorithm is also encouraging. 相似文献
15.
非线性约束最优化一族超线性收敛的可行方法 总被引:5,自引:0,他引:5
本文建立求解非线性不等式约束最优化一族含参数的可行方法.算法每次迭代仅需解一个规模较小的二次规划.在一定的假设条件下,证明了算法族的全局收敛性和超线性收敛性. 相似文献
16.
We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled
cyclic Barzilai–Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established
for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order
sufficient optimality conditions are satisfied. Numerical experiments show that the convergence speed is insensitive to problem
conditioning. The algorithm is particularly well suited for image restoration problems which arise in positron emission tomography
where the cost function can be infinite on the boundary of the feasible set.
This material is based upon work supported by the National Science Foundation under Grants 0203270, 0619080, and 0620286. 相似文献
17.
LIDONGHUI 《高校应用数学学报(英文版)》1996,11(4):487-496
In this paper, we propose an inexact clamped Newton method for solving nonlinear complementarity problems based on the equivalent B-differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given. 相似文献
18.
Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P
0-Functions 总被引:1,自引:0,他引:1
By using the Fischer–Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth
equations and using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing trust
region algorithm for solving the NCP with P
0 functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under
a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict
complementarity condition.
This work was partially supported by the Research Grant Council of Hong Kong and the National Natural Science Foundation of
China (Grant 10171030). 相似文献
19.
A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given. 相似文献
20.
Jin-Bao Jian Qing-Jie Hu Hai-Yan Zheng 《Numerical Functional Analysis & Optimization》2013,34(3-4):376-409
Combining the ideas of generalized projection and the strongly subfeasible sequential quadratic programming (SQP) method, we present a new strongly subfeasible SQP algorithm for nonlinearly inequality-constrained optimization problems. The algorithm, in which a new unified step-length search of Armijo type is introduced, starting from an arbitrary initial point, produces a feasible point after a finite number of iterations and from then on becomes a feasible descent SQP algorithm. At each iteration, only one quadratic program needs to be solved, and two correctional directions are obtained simply by explicit formulas that contain the same inverse matrix. Furthermore, the global and superlinear convergence results are proved under mild assumptions without strict complementarity conditions. Finally, some preliminary numerical results show that the proposed algorithm is stable and promising. 相似文献