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

目标。本项目的目标是基于先进的变分不等理论，对分布式认知分层和随后的网络体系结构分解进行系统和更好的理解。最终目标是开发一种新的方法来以分布式的方式来制定、研究和求解认知自组织网络的通用跨层设计(包括感知过程的优化)，建立在统称为分层变分不等的新框架上。智力上的功绩。变分不等式理论为许多有实际意义的公式提供了一个广泛的数学框架，如经典的非线性优化、均衡和博弈论问题。由此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而有力的平台，并为解决传统NUM设计中的基本问题提供了一个有前途的替代方向。拟议中的研究工作的成功可能会改变认知无线网络的教学和设计方式。这项研究将为复杂网络的设计提供高效、严格和成本效益高的新方法，这将代表着对当前基于启发式方法的转变。此外，该项目首次将变分不平等引入工程学科，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的相互促进，为这些社区的研究人员提供一个建设性和强大的平台，促进富有成效的发展。该研究项目由一个针对本科生和研究生的补充性教育项目完善。

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.