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The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. 相似文献
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遗传算法求解约束非线性规划及Matlab实现 总被引:4,自引:0,他引:4
对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性. 相似文献
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A penalty function approach for solving bi-level linear programs 总被引:8,自引:0,他引:8
The paper presents an approach to bi-level programming using a duality gap—penalty function format. A new exact penalty function exists for obtaining a global optimal solution for the linear case, and an algorithm is given for doing this, making use of some new theoretical properties. For each penalty parameter value, the central optimisation problem is one of maximising a convex function over a polytope, for which a modification of an algorithm of Tuy (1964) is used. Some numerical results are given. The approach has other features which assist the actual decisionmaking process, which make use of the natural roles of duality gaps and penalty parameters. The approach also allows a natural generalization to nonlinear problems. 相似文献
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S. Lucidi 《Journal of Optimization Theory and Applications》1990,67(2):227-245
An algorithm for nonlinear programming problems with equality constraints is presented which is globally and superlinearly convergent. The algorithm employs a recursive quadratic programming scheme to obtain a search direction and uses a differentiable exact augmented Lagrangian as line search function to determine the steplength along this direction. It incorporates an automatic adjustment rule for the selection of the penalty parameter and avoids the need to evaluate second-order derivatives of the problem functions. Some numerical results are reported. 相似文献
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多目标规划的一类基于精确罚函数的交互式方法 总被引:3,自引:0,他引:3
该文在约束集的线性化锥非空的条件下,得到了带有等式和不等式约束的多目标规划问题的精确罚函数的存在性,用原问题的二次近似在某些点上的Kuhn-Tucker乘子给出了罚因子的下界.在此基础上,利用极大熵方法的思想将罚问题转化为可微的无约束多目标规划问题并给出了求解该问题的一种交互式算法.数值结果表明:该文算法具有计算速度快、精度高、适用范围广且易于理解和使用等优点. 相似文献
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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
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' 1 IntroductionWe collsider the fOllowi11g bilevel programndng problen1:max f(x, y),(BP) s.t.x E X = {z E RnIAx = b,x 2 0}, (1)y e Y(x).whereY(x) = {argmaxdTyIDx Gy 5 g, y 2 0}, (2)and b E R", d, y E Rr, g E Rs, A, D.and G are m x n1 s x n aild 8 x r matrices respectively. If itis not very difficult to eva1uate f(and/or Vf) at all iteration points, there are many algorithmeavailable fOr solving problem (BP) (see [1,2,3etc1). However, in some problems (see [4]), f(x, y)is too com… 相似文献
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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
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《Optimization》2012,61(6):713-726
We describe a reduction algorithm for solving semi-infinite programming problems. The proposed algorithm uses the simulated annealing method equipped with a function stretching as a multi-local procedure, and a penalty technique for the finite optimization process. An exponential penalty merit function is reduced along each search direction to ensure convergence from any starting point. Our preliminary numerical results seem to show that the algorithm is very promising in practice. 相似文献
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在本文中,我们提出了带不等式约束的非线性规划问题的一类新的罚函数,它的一个子类可以光滑逼近$l_1$罚函数.
基于此类新的罚函数我们给出了一种罚算法,这个算法的特点是每次迭代求出罚函数的全局精确解或非精确解.
在很弱的条件下算法总是可行的.
我们在不需要任何约束规范的情况下,证明了算法的全局收敛性.
最后给出了数值实验. 相似文献
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M. Fernanda P. Costa Ana Maria A. C. Rocha Rogério B. Francisco Edite M. G. P. Fernandes 《Optimization》2016,65(5):1085-1104
In this article, we aim to extend the firefly algorithm (FA) to solve bound constrained mixed-integer nonlinear programming (MINLP) problems. An exact penalty continuous formulation of the MINLP problem is used. The continuous penalty problem comes out by relaxing the integrality constraints and by adding a penalty term to the objective function that aims to penalize integrality constraint violation. Two penalty terms are proposed, one is based on the hyperbolic tangent function and the other on the inverse hyperbolic sine function. We prove that both penalties can be used to define the continuous penalty problem, in the sense that it is equivalent to the MINLP problem. The solutions of the penalty problem are obtained using a variant of the metaheuristic FA for global optimization. Numerical experiments are given on a set of benchmark problems aiming to analyze the quality of the obtained solutions and the convergence speed. We show that the firefly penalty-based algorithm compares favourably with the penalty algorithm when the deterministic DIRECT or the simulated annealing solvers are invoked, in terms of convergence speed. 相似文献
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Rui Shen Zhiqing Meng Chuangyin Dang Min Jiang 《Numerical Functional Analysis & Optimization》2017,38(11):1473-1489
In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm. 相似文献
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本文通过给出的一个修正的罚函数,把约束非线性规划问题转化为无约束非线性规划问题.我们讨论了原问题与相应的罚问题局部最优解和全局最优解之间的关系,并给出了乘子参数和罚参数与迭代点之间的关系,最后给出了一个简单算法,数值试验表明算法是有效的. 相似文献
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本文给出了线性规划(LP)的解和其相应的精确罚函数解的等价性,证明是初等的,简明的。 相似文献