共查询到20条相似文献,搜索用时 15 毫秒
1.
J. B. Lasserre 《Operations Research Letters》1981,1(1):39-40
It has already been demonstrated that under some assumptions, a local minimum of a constrained problem is also a local unconstrained minimum of a function which is called an exact penalty function. Here, we present the same result with a new demonstration. By using sensitivity analysis, we give an economic interpretation for exact penalty functions. 相似文献
2.
In this work, we study a differentiable exact penalty function for solving twice continuously differentiable inequality constrained optimization problems. Under certain assumptions on the parameters of the penalty function, we show the equivalence of the stationary points of this function and the Kuhn-Tucker points of the restricted problem as well as their extreme points. Numerical experiments are presented that corroborate the theory, and a rule is given for choosing the parameters of the penalty function. 相似文献
3.
C. Charalambous 《Journal of Optimization Theory and Applications》1984,43(1):135-142
The purpose of this paper is to derive first-order necessary conditions for optimality of a class of nondifferentiable functions. The first-order necessary conditions for optimality for the minimax function and thel
1-function can be considered as special cases of the present method. Furthermore, the optimality conditions obtained are used to obtain threshold values for the controlling parameters of a class of exact penalty functions. 相似文献
4.
Krzysztof C. Kiwiel 《Mathematical Programming》1991,52(1-3):285-302
This paper presents new versions of proximal bundle methods for solving convex constrained nondifferentiable minimization problems. The methods employ
1 or
exact penalty functions with new penalty updates that limit unnecessary penalty growth. In contrast to other methods, some of them are insensitive to problem function scaling. Global convergence of the methods is established, as well as finite termination for polyhedral problems. Some encouraging numerical experience is reported. The ideas presented may also be used in variable metric methods for smooth nonlinear programming.This research was supported by the Polish Academy of Sciences. 相似文献
5.
6.
M. V. Dolgopolik 《Optimization》2017,66(10):1577-1622
In this article, we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions, and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parametric penalty functions, and derive necessary and sufficient conditions for a parametric penalty function to not have any stationary points outside the set of feasible points of the constrained optimization problem under consideration. In the second part of the paper, we apply the general theory of exact parametric penalty functions to a class of parametric penalty functions introduced by Huyer and Neumaier, and to smoothing approximations of nonsmooth exact penalty functions. The general approach adopted in this article allowed us to unify and significantly sharpen many existing results on parametric penalty functions. 相似文献
7.
《Optimization》2012,61(3-4):239-259
In this paper we propose a new class of continuously differentiable globally exact penalty functions for the solution of minimization problems with simple bounds on some (all) of the variables. The penalty functions in this class fully exploit the structure of the problem and are easily computable. Furthermore we introduce a simple updating rule for the penalty parameter that can be used in conjunction with unconstrained minimization techniques to solve the original problem. 相似文献
8.
In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported. 相似文献
9.
Stephen Wright 《Mathematical Programming》1989,44(1-3):221-234
We describe an inexact version of Fletcher's QL algorithm with second-order corrections for minimizing composite nonsmooth functions. The method is shown to retain the global and local convergence properties of the original version, if the parameters are chosen appropriately. It is shown how the inexact method can be implemented, for the case in which the function to be minimized is an exact penalty function arising from the standard nonlinear programming problem. The method can also be applied to the problems of nonlinearl
1 - andl
-approximation.This research supported in part by the National Science Foundation under Grant DMS-8619903, and by the Air Force Office of Scientific Research under Grant AFOSR-ISSA-870092. 相似文献
10.
对不等式约束优化问题提出了一个低阶精确罚函数的光滑化算法. 首先给出了光滑罚问题、非光滑罚问题及原问题的目标函数值之间的误差估计,进而在弱的假
设之下证明了光滑罚问题的全局最优解是原问题的近似全局最优解. 最后给出了一个基于光滑罚函数的求解原问题的算法,证明了算法的收敛性,并给出数值算例说明算法的可行性. 相似文献
11.
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
12.
J. F. A. De O. Pantoja D. Q. Mayne 《Journal of Optimization Theory and Applications》1991,69(3):441-467
A new globally convergent algorithm for minimizing an objective function subject to equality and inequality constraints is presented. The algorithm determines a search direction by solving a quadratic programming subproblem, which always has an optimal solution, and uses an exact penalty function to compute the steplength along this direction through an Armijo-type scheme. The special structure of the quadratic subproblem is exploited to construct a new and simple method for updating the penalty parameter. This method may increase or reduce the value of the penalty parameter depending on some easily performed tests. A new method for updating the Hessian of the Lagrangian is presented, and a Q-superlinear rate of convergence is established.This work was supported in part by the British Council and the Conselho Nacional de Desenvolvimento Cientifico & Tecnologico/CNPq, Rio de Janeiro, Brazil.The authors are very grateful to Mr. Lam Yeung for his invaluable assistance in computing the results and to a reviewer for constructive advice. 相似文献
13.
《Optimization》2012,61(6):829-838
An exact penalty approach for solving minimization problems with a concave objective function, linear constraints and Boolean variables is proposed. The penalty problems have continuous variables. An estimation of the penalty parameter which guarantees the exactness can be calculated on the base of an auxiliary problem. The results are applied to problems with an arbitrary quadratic objective function, linear constraints and Boolean variables. This leads to a modified Lagrangean approach for the latter problems. In the general case, the penalty approach is compared with a direct application of results of global optimization to a modification of the initial problem. 相似文献
14.
Y. Tanaka 《Journal of Optimization Theory and Applications》1988,59(1):147-151
In this note, lower bounds of penalty parameters of general exact penalty functions in locally Lipschitz programming are directly derived from Rosenberg's results. 相似文献
15.
Mihai Anitescu 《Mathematical Programming》2002,92(2):359-386
We analyze the convergence of a sequential quadratic programming (SQP) method for nonlinear programming for the case in which
the Jacobian of the active constraints is rank deficient at the solution and/or strict complementarity does not hold for some
or any feasible Lagrange multipliers. We use a nondifferentiable exact penalty function, and we prove that the sequence generated
by an SQP using a line search is locally R-linearly convergent if the matrix of the quadratic program is positive definite
and constant over iterations, provided that the Mangasarian-Fromovitz constraint qualification and some second-order sufficiency
conditions hold.
Received: April 28, 1998 / Accepted: June 28, 2001?Published online April 12, 2002 相似文献
16.
对约束优化问题给出了一类光滑罚算法.它是基于一类光滑逼近精确罚函数 l_p(p\in(0,1]) 的光滑函数 L_p 而提出的.在非常弱的条件下, 建立了算法的一个摄动定理, 导出了算法的全局收敛性.特别地, 在广义Mangasarian-Fromovitz约束规范假设下, 证明了当 p=1 时, 算法经过有限步迭代后, 所有迭代点都是原问题的可行解; p\in(0,1) 时,算法经过有限迭代后, 所有迭代点都是原问题可行解集的内点. 相似文献
17.
A sequential quadratic programming algorithm for nonlinear programs using anl
-exact penalty function is described. Numerical results are also presented. These results show that the algorithm is competitive with other exact penalty function based algorithms and that the inclusion of the second penalty parameter can be advantageous. 相似文献
18.
M. V. Dolgopolik 《Optimization》2016,65(6):1167-1202
In this article, we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally exact linear penalty functions, and obtain various necessary and sufficient conditions for the exactness of a linear penalty function. We pay more attention than usual to necessary conditions, which allows us to deeply understand the exact penalty technique. 相似文献
19.
An exact penalty function method with global convergence properties for nonlinear programming problems 总被引:3,自引:0,他引:3
In this paper a new continuously differentiable exact penalty function is introduced for the solution of nonlinear programming
problems with compact feasible set. A distinguishing feature of the penalty function is that it is defined on a suitable bounded
open set containing the feasible region and that it goes to infinity on the boundary of this set. This allows the construction
of an implementable unconstrained minimization algorithm, whose global convergence towards Kuhn-Tucker points of the constrained
problem can be established. 相似文献
20.
D. J. White 《Journal of Optimization Theory and Applications》1993,78(2):283-301
In this paper, we provide the theoretical foundations of an extension of the Frank-Wolfe algorithm for concave continuously differentiable objective functions to concave nondifferentiable objective functions, using a subgradient approach. The main theorem extends the results of Frank and Wolfe. A key main assumption is examined in the context of some special cases via three lemmas. A comparison is made with other subgradient approaches, and consideration is given to the two subproblem optimizations arising in the modified algorithm.This work was carried out under the auspices of the University of Manchester, Manchester, England. The author thanks the referees for their very helpful comments on the original version. 相似文献