共查询到20条相似文献,搜索用时 15 毫秒
1.
T. Antczak 《Journal of Optimization Theory and Applications》2013,159(2):437-453
In the paper, we consider the exact minimax penalty function method used for solving a general nondifferentiable extremum problem with both inequality and equality constraints. We analyze the relationship between an optimal solution in the given constrained extremum problem and a minimizer in its associated penalized optimization problem with the exact minimax penalty function under the assumption of convexity of the functions constituting the considered optimization problem (with the exception of those equality constraint functions for which the associated Lagrange multipliers are negative—these functions should be assumed to be concave). The lower bound of the penalty parameter is given such that, for every value of the penalty parameter above the threshold, the equivalence holds between the set of optimal solutions in the given extremum problem and the set of minimizers in its associated penalized optimization problem with the exact minimax penalty function. 相似文献
2.
Bingzhuang Liu 《Journal of Applied Mathematics and Computing》2009,30(1-2):259-270
In the paper, we give a smoothing approximation to the nondifferentiable exact penalty function for nonlinear constrained optimization problems. Error estimations are obtained among the optimal objective function values of the smoothed penalty problems, of the nonsmooth penalty problem and of the original problem. An algorithm based on our smoothing function is given, which is showed to be globally convergent under some mild conditions. 相似文献
3.
Tadeusz Antczak Marcin Studniarski 《Numerical Functional Analysis & Optimization》2016,37(12):1465-1487
In this article, the vector exact l1 penalty function method used for solving nonconvex nondifferentiable multiobjective programming problems is analyzed. In this method, the vector penalized optimization problem with the vector exact l1 penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penalized optimization problem with the vector exact l1 penalty function. This equivalence is established for nondifferentiable invex vector optimization problems. Some examples of vector optimization problems are presented to illustrate the results established in the article. 相似文献
4.
Tadeusz Antczak 《Optimization Letters》2016,10(7):1561-1576
In this paper, it is demonstrated that the exact absolute value penalty function method is useful for identifying the special sort of minimizers in nonconvex nonsmooth optimization problems with both inequality and equality constraints. The equivalence between the sets of strict global minima of order m in nonsmooth minimization problem and of its associated penalized optimization problem with the exact \(l_{1}\) penalty function is established under nondifferentiable \(\left( F,\rho \right) \)-convexity assumptions imposed on the involved functions. The threshold of the penalty parameter, above which this result holds, is also given. 相似文献
5.
《Operations Research Letters》2022,50(5):602-609
In this study, a gH-penalty method is developed to obtain efficient solutions to constrained optimization problems with interval-valued functions. The algorithmic implementation of the proposed method is illustrated. In order to develop the gH-penalty method, an interval-valued penalty function is defined and the characterization of efficient solutions of a CIOP is done. As an application of the proposed method, a portfolio optimization problem with interval-valued return is solved. 相似文献
6.
赵可昳 《高等学校计算数学学报》1998,20(4):321-328
1引言 在约束最优化的研究中,罚函数法有很高的理论及应用价值,为求约束优化问题的最优解x,很多方法是通过求解一系列优化问题来实现,人们称之为SUMT方法~[1]. 相似文献
7.
Global convergence of a semi-infinite optimization method 总被引:1,自引:0,他引:1
Bradley M. Bell 《Applied Mathematics and Optimization》1990,21(1):69-88
A new algorithm for minimizing locally Lipschitz functions using approximate function values is presented. It yields a method for minimizing semi-infinite exact penalty functions that parallels the trust-region methods used in composite nondifferentiable optimization. A finite method for approximating a semi-infinite exact penalty function is developed. A uniform implicit function theorem is established during this development. An implementation and test results for the approximate penalty function are included. 相似文献
8.
Bin Li Chang Jun Yu Kok Lay Teo Guang Ren Duan 《Journal of Optimization Theory and Applications》2011,151(2):260-291
In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous
state and control inequality constraints. By using the control parametrization technique and a time scaling transformation,
the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality
terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection
problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints.
On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems
with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed
from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives
rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value,
any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality
constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with
equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For
illustration, three examples are solved showing the effectiveness and applicability of the approach proposed. 相似文献
9.
10.
Zhiqing Meng Chuangyin Dang Xiaoqi Yang 《Computational Optimization and Applications》2006,35(3):375-398
In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained
optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem,
of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization
problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed
penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient. 相似文献
11.
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
12.
Lian-Sheng Zhang 《计算数学(英文版)》1988,6(4):375-382
We give an approach for finding a global minimization with equality and inequality Constraints.Our approach is to construct an exact penalty function, and prove that the global minimal points of this exact penalty function are the primal constrained global minimal points. Thus we convert the problem of global constrained optimization into a problem of global unconstrained optimization. Furthermore, the integral approach for finding a global minimization for a class of discontinuous functions is used and an implementable algorithm is given. 相似文献
13.
带等式约束的光滑优化问题的一类新的精确罚函数 总被引:1,自引:0,他引:1
罚函数方法是将约束优化问题转化为无约束优化问题的主要方法之一. 不包含目标函数和约束函数梯度信息的罚函数, 称为简单罚函数. 对传统精确罚函数而言, 如果它是简单的就一定是非光滑的; 如果它是光滑的, 就一定不是简单的. 针对等式约束优化问题, 提出一类新的简单罚函数, 该罚函数通过增加一个新的变量来控制罚项. 证明了此罚函数的光滑性和精确性, 并给出了一种解决等式约束优化问题的罚函数算法. 数值结果表明, 该算法对于求解等式约束优化问题是可行的. 相似文献
14.
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
15.
Jane J. Ye 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1642-1654
The exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem, and the reverse property is rarely studied. In this paper, we study the reverse property. We give the conditions under which the original constrained (single and/or multiobjective) optimization problem and the unconstrained exact penalized problem are exactly equivalent. The main conditions to ensure the exact penalty principle for optimization problems include the global and local error bound conditions. By using variational analysis, these conditions may be characterized by using generalized differentiation. 相似文献
16.
Canghua Jiang Qun Lin Changjun Yu Kok Lay Teo Guang-Ren Duan 《Journal of Optimization Theory and Applications》2012,154(1):30-53
In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method. 相似文献
17.
Anurag Jayswal Manuel Arana-Jiménez 《Journal of Mathematical Analysis and Applications》2022,505(1):125453
This paper gives some new results on multi-time first-order PDE constrained control optimization problem in the face of data uncertainty (MCOPU). We obtain the robust sufficient optimality conditions for (MCOPU). Further, we construct an unconstrained multi-time control optimization problem (MCOPU)? corresponding to (MCOPU) via absolute value penalty function method. Then, we show that the robust optimal solution to the constrained problem and a robust minimizer to the unconstrained problem are equivalent under suitable hypotheses. Moreover, we give some non-trivial examples to validate the results established in this paper. 相似文献
18.
19.
Xinsheng Xu Chuangyin Dang Felix T. S. Chan Yongli Wang 《Numerical Functional Analysis & Optimization》2019,40(1):1-18
This article introduces a smoothing technique to the l1 exact penalty function. An application of the technique yields a twice continuously differentiable penalty function and a smoothed penalty problem. Under some mild conditions, the optimal solution to the smoothed penalty problem becomes an approximate optimal solution to the original constrained optimization problem. Based on the smoothed penalty problem, we propose an algorithm to solve the constrained optimization problem. Every limit point of the sequence generated by the algorithm is an optimal solution. Several numerical examples are presented to illustrate the performance of the proposed algorithm. 相似文献