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

目标。该项目的目标是在变分不等式先进理论的基础上，对分布式认知分层和随之而来的网络架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，以分布式的方式制定、研究和解决认知自组织网络的通用跨层设计（包括感知过程的优化），建立在一个统称为分层变分不等式的新框架上。知识价值。变分不等式的理论提供了一个广泛的数学框架，许多公式的实际利益，如经典的非线性优化，平衡和博弈论问题。因此，提出的分层变分不等式问题为研究几种新的跨层设计提供了一个建设性和强大的平台，并为处理传统NUM设计的基本问题提供了另一种有前途的方向。更广泛的影响。这项研究的成功有可能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、严谨和具有成本效益的新方法，这将代表着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，将促进不同研究领域之间的交流，如信号处理、优化、博弈和决策理论以及网络，为这些社区的研究人员提供一个富有成果的建设性和强大的平台。该研究项目是由一个针对本科生和研究生的补充教育计划完善的。

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.