THE NONLINEAR BILEVEL PROGRAMMING PROBLEM: FORMULATIONS, REGULARITY AND OPTIMALITY CONDITIONS
THE NONLINEAR BILEVEL PROGRAMMING PROBLEM: FORMULATIONS, REGULARITY AND OPTIMALITY CONDITIONS
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DOI：
10.1080/02331939508844048
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发表时间：
1993-07
期刊：
影响因子：
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通讯作者：
Yao Chen;M. Florian
中科院分区：
文献类型：
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作者：
Yao Chen;M. Florian
本文利用一个新提出的边际函数公式，研究了BLPP的正则性和最优性条件，其中边际函数si由下层问题的最优值函数定义。他们通过探索BLPP可行集的切锥结构来解决正则性问题。这些规律性结果表明，非线性/非线性BLPP极有可能是退化的，而非线性/线性BLPP在常规意义上是规则的。证明了一类非线性/线性BLPP的精确惩罚函数的存在性。在非光滑分析的框架下，导出了一般非线性BLPP的Fritz-John型最优性条件，得到了一类非线性/线性BLPP的KKT型最优性条件。文中给出了一个典型实例，并指出了这些条件的一些应用。(一)
In this paper, the authors study regularity and optimality conditions for the BLPP by using a newly proposed marginal function formulation, where the marginal function si defined by the optimal value function of the lower level problem. They address the regularity issue by exploring the structure of the tangent cones of the feasible set of the BLPP. These regularity results indicate that the nonlinear/nonlinear BLPP is most likely degenerate and the nonlinear/linear BLPP is regular in the conventional sense. Existence of exact penalty function is proved for a class of nonlinear/linear BLPP. Fritz-John type optimality conditions are derived for general nonlinear BLPP in the framework of nonsmooth analysis, while KKT type optimality conditions are obtained for a class of nonlinear/linear BLPP. A typical example is examined for these conditions and some applications of these conditions are pointed out. (A)