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不等式约束二次规划的一新算法 总被引:3,自引:0,他引:3
文献[1]提出了一般等式约束非线性规划问题一种求解途径.文献[2]应用这一途径给出了等式约束二次规划问题的一种算法,本文在文献[1]和[2]的基础上对不等式约束二次规划问题提出了一种新算法. 相似文献
3.
A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming. By using an interior-point method to accommodate inequality constraints, a modification of an existing algorithm for equality constrained problems can be used iteratively to solve the subproblems. Two test problems and two application problems are presented. The application examples include a rest-to-rest maneuver of a flexible structure and a constrained brachistochrone problem. 相似文献
4.
In this paper, the feasible type SQP method is improved. A new SQP algorithm is presented to solve the nonlinear inequality constrained optimization. As compared with the existing SQP methods, per single iteration, in order to obtain the search direction, it is only necessary to solve equality constrained quadratic programming subproblems and systems of linear equations. Under some suitable conditions, the global and superlinear convergence can be induced. 相似文献
5.
A recursive quadratic programming algorithm that uses differentiable exact penalty functions 总被引:8,自引:0,他引:8
In this paper, a recursive quadratic programming algorithm for solving equality constrained optimization problems is proposed and studied. The line search functions used are approximations to Fletcher's differentiable exact penalty function. Global convergence and local superlinear convergence results are proved, and some numerical results are given. 相似文献
6.
S. Zhang 《Journal of Optimization Theory and Applications》1994,82(1):121-138
In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity, called the harmonic convexity in this paper. A characterization of this convexity condition is given. The same convexity condition was used by Mehrotra and Sun to prove the convergence of a path-following algorithm.The Iri-Imai algorithm is a natural generalization of the original Newton algorithm to constrained convex programming. Other known convergent interior-point algorithms for smooth convex programming are mainly based on the path-following approach. 相似文献
7.
This paper presents a primal-dual interior-point algorithm for solving general constrained nonlinear programming problems. The inequality constraints are incorporated into the objective function by means of a logarithmic barrier function. Also, satisfaction of the equality constraints is enforced through the use of an adaptive quadratic penalty function. The penalty parameter is determined using a strategy that ensures a descent property for a merit function. Global convergence of the algorithm is achieved through the monotonic decrease of a merit function. Finally, extensive computational results show that the algorithm can solve large and difficult problems in an efficient and robust way.Communicated by L. C. W. DixonThe research reported in this paper was done while the first author was at Imperial College. The authors gratefully acknowledge constructive comments from Professor L. C. W. Dixon and an anonymous referee. They are also grateful to Dr. Stanislav Zakovic for helpful suggestions and comments. Financial support was provided by EPSRC Grants M16016 and GR/G51377/01. 相似文献
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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. 相似文献
10.
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
11.
Michael J. Best 《Mathematical Programming》1984,30(1):71-87
We formulate a general algorithm for the solution of a convex (but not strictly convex) quadratic programming problem. Conditions
are given under which the iterates of the algorithm are uniquely determined. The quadratic programming algorithms of Fletcher,
Gill and Murray, Best and Ritter, and van de Panne and Whinston/Dantzig are shown to be special cases and consequently are
equivalent in the sense that they construct identical sequences of points. The various methods are shown to differ only in
the manner in which they solve the linear equations expressing the Kuhn-Tucker system for the associated equality constrained
subproblems. Equivalence results have been established by Goldfarb and Djang for the positive definite Hessian case. Our analysis
extends these results to the positive semi-definite case.
This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A8189. 相似文献
12.
In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. 相似文献
13.
We propose an algorithm for the constrained continuous minimax problem. The algorithm uses a quasi-Newton search direction,
based on subgradient information, conditional on maximizers. The initial problem is transformed to an equivalent equality
constrained problem, where the logarithmic barrier function is used to ensure feasibility. In the case of multiple maximizers,
the algorithm adopts semi-infinite programming iterations toward epiconvergence. Satisfaction of the equality constraints
is ensured by an adaptive quadratic penalty function. The algorithm is augmented by a discrete minimax procedure to compute
the semi-infinite programming steps and ensure overall progress when required by the adaptive penalty procedure. Progress
toward the solution is maintained using merit functions. 相似文献
14.
魏紫銮 《应用数学学报(英文版)》2001,17(3):366-374
1. IntroductionThe quadratic programming (QP) problem is the most simple one in nonlinear pro-gramming and plays a very important role in optimization theory and applications.It is well known that matriX splitting teChniques are widely used for solving large-scalelinear system of equations very successfully. These algorithms generate an infinite sequence,in contrast to the direct algorithms which terminate in a finite number of steps. However,iterative algorithms are considerable simpler tha… 相似文献
15.
Alfred Auslender 《Journal of Optimization Theory and Applications》2013,156(2):183-212
This paper is concerned with nonlinear, semidefinite, and second-order cone programs. A general algorithm, which includes sequential quadratic programming and sequential quadratically constrained quadratic programming methods, is presented for solving these problems. In the particular case of standard nonlinear programs, the algorithm can be interpreted as a prox-regularization of the Solodov sequential quadratically constrained quadratic programming method presented in Mathematics of Operations Research (2004). For such type of methods, the main cost of computation amounts to solve a linear cone program for which efficient solvers are available. Usually, “global convergence results” for these methods require, as for the Solodov method, the boundedness of the primal sequence generated by the algorithm. The other purpose of this paper is to establish global convergence results without boundedness assumptions on any of the iterative sequences built by the algorithm. 相似文献
16.
C. Ling L. Q. Qi G. L. Zhou S. Y. Wu 《Journal of Optimization Theory and Applications》2006,129(1):147-164
The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth
nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the
integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome
this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth
nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always
feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are
given.
Communicated by F. Giannessi
His work was supported by the Hong Kong Research Grant Council
His work was supported by the Australian Research Council. 相似文献
17.
On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization 下载免费PDF全文
A trust-region sequential quadratic programming (SQP) method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the transposition of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported. 相似文献
18.
A globally convergent trust region algorithm for optimization with general constraints and simple bounds 总被引:3,自引:0,他引:3
1.IntroductionInthispaper,weconsiderthefollowingnonlinearprogr~ngproblemwherec(x)=(c,(x),c2(2),',We(.))',i(x)andci(x)(i=1,2,',m)arerealfunctions*ThisworkissupPOrtedbytheNationalNaturalScienceFOundationofChinaandtheManagement,DecisionandinformationSystemLab,theChineseAcademyofSciences.definedinD={xEReIISx5u}.Weassumethath相似文献
19.
Wenjuan Xue & Weiai Liu 《计算数学(英文版)》2020,38(5):683-704
We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrained
optimization problems. In our proposed algorithm, the constraints are partitioned into
several parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each part
of constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. The
other is that feasibility restoration phases are unnecessary because a consistent quadratic
programming subproblem is used. We prove that our algorithm is globally convergent to
KKT points under the constant positive generators (CPG) condition which is weaker than
the well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant
positive linear dependence (CPLD). Numerical results are presented to show the efficiency
of the algorithm. 相似文献
20.
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