A quadratic objective penalty function for bilevel programming
A quadratic objective penalty function for bilevel programming
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DOI：
10.1007/s11424-014-2128-7
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发表时间：
2014-04
影响因子：
2.1
通讯作者：
M. Jiang;Z. Meng;R. Shen;Xinsheng Xu
中科院分区：
文献类型：
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作者：
M. Jiang;Z. Meng;R. Shen;Xinsheng Xu
将双层规划应用于解决工业、农业、交通、军事等领域的递阶智能控制问题。本文给出了一个带有两个惩罚参数的二次目标罚函数，该函数是一个带有两个罚参数的二次目标罚函数。在一定条件下，证明了二次目标罚函数所定义的二层规划的最优解是原二层规划的最优解。此外，基于二次目标惩罚函数，给出了一个求解原双层规划最优解的算法，并在一定条件下证明了该算法的收敛性。在下层问题凸的假设下，定义了一个无下层问题的二次目标罚函数，并证明了它与原双层规划是等价的。
The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.