Solution algorithms for bilevel optimization problems

双层优化问题是一类特殊的具有两层递阶结构的优化问题。在许多应用中，当所谓的上层和下层的决策过程相互依赖时，这种结构自然而频繁地出现。双层优化的应用包括但不限于运输、管理、化学、环境问题、经济和工程。然而，双层规划是非常困难的解决，它实际上是NP-难，非凸和非光滑。此外，最优化理论中大多数著名的约束条件并不成立。这个研究项目的主要目标是开发严格的解决方案的算法，适合于乐观的双层计划，允许在较低级别的问题有一个以上的最优解。凸和非凸的情况下，将分别通过KKT和LLVF的重新制定，并将这两种方法进行比较。

The bilevel optimization problem is a special class of optimization problem having a two-level hierarchical structure. Such structures arise naturally and frequently in many applications when the decision processes in the so-called upper and lower levels are interdependent. Applications of bilevel optimization include and are not limited to transportation, management, chemistry, environmental issues, economics and engineering. However, the bilevel program is very difficult to solve; it is in fact NP-hard, nonconvex and nonsmooth. Moreover, most of the well-known constraint qualifications in optimization theory do not hold. The main goal of this research project is to develop rigorous solution algorithms tailored to optimistic bilevel programs allowing more than one optimal solution in the lower-level problem. The convex and nonconvex cases will be investigated via the KKT and LLVF reformulations, respectively, and both approaches will be compared.