CAREER:Variational Inequalities: A New Paradigm for Cognitive Network Layering

Objective. 该项目的目标是在变分不等式先进理论的基础上，系统地更好地理解分布式认知分层和随之而来的网络架构分解。最终目标是开发一种新的方法来制定，研究和解决在分布式的方式通用的跨层设计的认知ad-hoc网络（包括传感过程的优化），建立在一个新的框架，统称为层次变分不等式。智力优势。变分不等式理论提供了一个广泛的数学框架，用于解决许多实际问题，如经典的非线性优化、均衡和博弈论问题。 因此，本文提出的分层变分不等式问题为研究几种新颖的跨层设计提供了一个建设性的、强大的平台，并为解决传统NUM设计的基本问题提供了一个替代的、有前途的方向。在拟议的研究工作的成功有可能改变如何教和设计认知无线网络。这项研究将为复杂网络的设计提供高效，严格和具有成本效益的新方法，这将代表当前基于启发式方法的转变。此外，该项目首次将变分不等式引入工程学科，将促进信号处理、优化、博弈和决策理论以及网络等不同研究领域之间的交叉交流，为这些社区的研究人员提供一个建设性的强大平台，以实现富有成效的发展。该研究项目是由一个互补的教育计划，目标是本科生和研究生。

Objective. The goal of this project is to progress towards a systematic and better understanding of distributed cognitive layering and consequent network architecture decompositions, based on the advanced theory of Variational Inequalities. The ultimate objective is developing a new methodology to formulate, study, and solve in a distributed way generic cross-layer designs of cognitive ad-hoc networks (including the optimization of the sensing process), building on a novel framework that collectively is termed hierarchical Variational Inequalities. Intellectual Merit. The theory of Variational Inequalities provides a broad mathematical framework for a host of formulations of practical interest, such as classical nonlinear optimization, equilibrium, and game-theoretic problems. The proposed hierarchical Variational Inequality problem offers thus a constructive and powerful platform to investigate several novel cross-layer designs, and provides an alternative and promising direction to deal with the fundamental issues of traditional NUM designs.Broader Impact. Success in the proposed research effort has the potential to change how to teach and design cognitive wireless networks. This research will enable efficient, rigorous, and cost-effective new approaches for the design of complex networks, which will represent a shift from current heuristic based approaches. Moreover, bringing for the first time Variational Inequalities in engineering disciplines, the project will promote cross-fertilization among different research fields, such as signal processing, optimization, game and decision theory, and networking, offering to researchers in these communities a constructive and powerful platform for fruitful developments. The research project is well rounded by a complementary educational program that targets both undergraduate and graduate students.