Applications, Algorithms and Extensions of Complementarity

在过去的几年里，已经开发了几种用于解决非线性混合互补问题的健壮算法，以及旨在使使用互补框架的应用的研究人员能够访问这些算法的软件。本提案旨在通过考虑跨学科背景下的互补性建模的完整解决方案过程来继续和扩展这项工作。该提案的重点是开发新的实用计算方法，这些方法将有力地解决大型工程和经济问题，这些问题将作为本提案的一部分，与应用专家协商制定。与迄今已执行的大部分算法工作不同，解算器将使用特殊用途的技术来增强，这些技术将试图自动将模型转换为算法上有利的形式，并诊断给定模型中的缺陷。这将使许多应用程序能够更快地求解，因为算法的求解时间通常比开发、修改和改进底层模型所花费的时间短得多。将确保正在开发的算法和工具是通用的，易于使用，并尽可能为算法的用户提供信息。与几个应用领域的专家的直接互动将决定如何使用互补的概念简洁地模拟各种物理现象。以及提供将非线性程序转换为混合互补问题的自动翻译机制。该项目将解决在经济学和结构工程中的断裂问题中综合评估模型的补充框架的使用问题。

Over the past few years, several robust algorithms have been developed for solving nonlinear mixed complementarity problems, along with software aimed at making these algorithms accessible to researchers with applications that employ the complementarity framework. This proposal aims to continue and extend this work by considering the complete solution process for complementarity modeling in an interdisciplinary setting. The emphasis of the proposal is on developing new practical computational methods that will robustly solve the large-scale engineering and economic problems that will be formulated as part of this proposal in consultation with application experts. In contrast to much of the algorithm work that has been carried out to date, the solvers will be augmented with special purpose techniques that will attempt to automatically convert models to algorithmically advantageous forms and to diagnose deficiences in a given model. This will enable much quicker solution of many applications, since the solution time of an algorithm is typically much less that the time taken to develop, modify and refine the underlying models. It will be ensured that the algorithms and tools being developed are general purpose, easy to use and as informative to the user of the algorithms as possible. A direct interaction with experts in several application areas will determine how various physical phenomenon can be succinctly modeled using the notion of complementarity. As well as providing an automatic translation mechanism to convert nonlinear programs into mixed complementarity problems. The project will address the use of the complementarity framework for integrated assessment models in economics and fracture problems in structural engineering.