共查询到18条相似文献,搜索用时 218 毫秒
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研究了线性半向量二层规划问题的全局优化方法. 利用下层问题的对偶间隙构造了线性半向量二层规划问题的罚问题, 通过分析原问题的最优解与罚问题可行域顶点之间的关系, 将线性半向量二层规划问题转化为有限个线性规划问题, 从而得到线性半向量二层规划问题的全局最优解. 数值结果表明所设计的全局优化方法对线性半向量二层规划问题是可行的. 相似文献
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下层多目标规划问题的Pareto最优解的精确性对于成功求解半向量二层规划问题具有决定性作用.本文基于多目标规划问题的KKT背离度量方程,设计了具有确定性终止准则的半向量二层规划问题的粒子群算法.最后,利用线性半向量二层规划算例和非线性半向量二层规划算例进行数值仿真,仿真结果表明,算法中的KKT背离度量方程能有效控制下层问题Pareto最优解的精度,从而确保问题最优解的真实有效性. 相似文献
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文章研究了一类结构为非线性-线性-线性三:层规划问题的求解方法.首先,基于下层问题的Karush-Kuhn-Tucker (K-K-T)最优性条件,将该类非线性三层规划问题转化为具有互补约束的非线性二层规划,同时将下层问题的互补约束作为罚项添加到上层目标;然后,再次利用下层问题的K-K-T最优性条件将非线性二层规划转化为非线性单层规划,并再次将得到的互补约束作为上层目标的罚项,构造了该类非线性三层规划问题的罚问题.通过对罚问题性质的分析,得到了该类非线性三层规划问题最优解的必要条件,并设计了罚函数算法.数值结果表明所设计的罚函数算法是可行、有效的. 相似文献
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本文研究了一类非线性-线性半向量二层规划问题的罚函数求解方法.对于该类半向量二层规划问题,首先基于下层问题的加权标量化方法和Karush-Kuhn-Tucker最优性条件,将其转化为一般的二层规划问题,并取下层问题的互补约束为罚项,构造出相应的罚问题;然后分析罚问题最优解的相关特征以及最优性条件,进而设计了相应的罚函数算法;最后以相关算例验证了罚函数算法的可行、有效性. 相似文献
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We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples. 相似文献
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In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem. 相似文献
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J. Glackin J. G. Ecker M. Kupferschmid 《Journal of Optimization Theory and Applications》2009,140(2):197-212
We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm
uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing
a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed
are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound
algorithm when the number of leader variables is small. 相似文献
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Weak linear bilevel programming problems: existence of solutions via a penalty method 总被引:1,自引:0,他引:1
Abdelmalek Aboussoror Abdelatif Mansouri 《Journal of Mathematical Analysis and Applications》2005,304(1):399-408
We are concerned with a class of weak linear bilevel programs with nonunique lower level solutions. For such problems, we give via an exact penalty method an existence theorem of solutions. Then, we propose an algorithm. 相似文献
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In this paper, we consider a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint and the upper level program has a convex set constraint. By using the value function of the lower level program, we reformulate the bilevel program as a single level optimization problem with a nonsmooth inequality constraint and a convex set constraint. To deal with such a nonsmooth and nonconvex optimization problem, we design a smoothing projected gradient algorithm for a general optimization problem with a nonsmooth inequality constraint and a convex set constraint. We show that, if the sequence of penalty parameters is bounded then any accumulation point is a stationary point of the nonsmooth optimization problem and, if the generated sequence is convergent and the extended Mangasarian-Fromovitz constraint qualification holds at the limit then the limit point is a stationary point of the nonsmooth optimization problem. We apply the smoothing projected gradient algorithm to the bilevel program if a calmness condition holds and to an approximate bilevel program otherwise. Preliminary numerical experiments show that the algorithm is efficient for solving the simple bilevel program. 相似文献
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In this paper, we prove that an optimal solution to the linear fractional bilevel programming problem occurs at a boundary feasible extreme point. Hence, the Kth-best algorithm can be proposed to solve the problem. This property also applies to quasiconcave bilevel problems provided that the first level objective function is explicitly quasimonotonic. 相似文献
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In this paper, we address a class of semivectorial bilevel programming problem in which the upper level is a scalar optimization problem and the lower level is a linear multi-objective optimization problem. Then, we present a new penalty function method, which includes two different penalty parameters, for solving such a problem. Furthermore, we give a simple algorithm. Numerical examples show that the proposed algorithm is feasible. 相似文献