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

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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.