SIAM Journal on Optimization, Volume 31, Issue 1, Page 275-306, January 2021.
In this study, we consider a rich class of mathematical programs with equilibrium constraints (MPECs) involving both integer and continuous variables. Such a class, which subsumes mathematical programs with complementarity constraints, as well as bilevel programs involving lower level convex programs is, in general, extremely hard to solve due to complementarity constraints and integrality requirements. For its solution, we design an (exact) algorithmic framework based on branch-and-bound (B&B) that treats each node of the B&B tree as a separate optimization problem and potentially changes its formulation and solution approach by designing, for example, a separate B&B tree. The framework is implemented and computationally evaluated on a specific instance of MPEC, namely a competitive facility location problem that takes into account the queueing process that determines the equilibrium assignment of users to open facilities, and a generalization of models for which, to date, no exact method has been proposed.

中文翻译：

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一类具有均衡约束的混合整数程序的精确算法框架

SIAM优化杂志，第31卷，第1期，第275-306页，2021年1月。
在这项研究中，我们考虑一类丰富的数学程序，它们具有涉及整数和连续变量的平衡约束（MPEC）。通常，由于互补性约束和完整性要求，这种包含了互补性约束的数学程序以及涉及较低级凸型程序的双层程序的类通常极难解决。对于其解决方案，我们设计了一种基于分支定界（B＆B）的（精确）算法框架，该框架将B＆B树的每个节点视为一个单独的优化问题，并可能通过设计（例如）单独的B＆B树。该框架是在MPEC的特定实例上实施和计算评估的，