Multilevel optimization problems with nonconvexities and their applications to smart-grids

双向和更一般的多级优化问题是一个非常通用的工具，多个竞争的演员建模的问题。一个经典的例子是双层问题，发生在定价方案的设计，如能源市场。具有凸下层的两层问题的求解方法已经得到了很好的理解，但仍然具有挑战性。引入非凸性到较低的水平（如整数变量或非线性等式），使这些问题在计算上难以解决的实际应用。对于特定应用，特设方法是已知的。我们的目标是进一步的理论和开发算法，这些问题的子类，可以应用到智能电网的定价问题。

Bi- and more general multilevel optimization problems are a very versatile tool to model problems with multiple competing actors. A classical example are bilevel problems that occur in the design of pricing schemes in eg energy markets. Solution methods for bilevel problems with convex lower level are well understood, nevertheless they remain challenging. Introducing nonconvexities into the lower level (eg integer variables or nonlinear equalities) makes these problems computationally intractable for practical applications. For specific applications, ad hoc methods are known. The goal is to further the theory and develop algorithms for subclasses of these problems that can be applied to pricing problems in smart-grids.