Exact Penalization of Mathematical Programs with Equilibrium Constraints
Exact Penalization of Mathematical Programs with Equilibrium Constraints
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DOI：
10.1137/s0363012996306121
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发表时间：
1999-02
影响因子：
2.2
通讯作者：
S. Scholtes;M. Stöhr
中科院分区：
文献类型：
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作者：
S. Scholtes;M. Stöhr
我们研究具有平衡约束（MPEC）的数学程序的精确惩罚方法的理论和计算方面。在第一部分中，我们证明 Mangasarian-Fromovitz 型条件确保实值非负分段平滑函数的根处存在稳定的局部误差界。对平衡约束的非光滑公式（例如互补条件或正规方程）的规范提供了保证 MPEC 存在非光滑精确罚函数的条件。在第二部分中，我们研究了一类复合非光滑函数的信赖域最小化方法，该函数包含由 MPEC 产生的精确惩罚函数。我们证明了通用方法的全局收敛结果并结合了惩罚更新规则。进一步的规范产生了基于 \(\ell_1\) 惩罚函数的 MPEC 的 SQP 信任域方法。
We study theoretical and computational aspects of an exact penalization approach to mathematical programs with equilibrium constraints (MPECs). In the first part, we prove that a Mangasarian--Fromovitz-type condition ensures the existence of a stable local error bound at the root of a real-valued nonnegative piecewise smooth function. A specification to nonsmooth formulations of equilibrium constraints, e.g., complementarity conditions or normal equations, provides conditions which guarantee the existence of a nonsmooth exact penalty function for MPECs. In the second part, we study a trust region minimization method for a class of composite nonsmooth functions which comprises exact penalty functions arising from MPECs. We prove a global convergence result for the general method and incorporate a penalty update rule. A further specification results in an SQP trust region method for MPECs based on an \(\ell_1\) penalty function.