Variational Inequality (VI) Methods for Multiuser Communication Systems and Smart Grids

The Variation Inequality (VI) problem constitutes a very general class of problems in nonlinear analysis. The VI framework embraces many different types of problems such as systems of equations, optimization problems, equilibrium programming, complementary problems, saddle-point problems, Nash equilibrium problems, and generalized Nash equilibrium problems. It specially bears strong connections with game theory. There is a well-developed theory for the analysis of solutions of VIs, as well as a wide variety of efficient algorithms with convergence properties. Therefore, it constitutes an excellent tool for analyzing the previous problems and, in particular, game problems where the classical game-theoretic tools may fall short like in advanced cognitive radio systems.

Papers

• Gesualdo Scutari, Francisco Facchinei, Jong-Shi Pang, and Daniel P. Palomar, “Real and Complex Monotone Communication Games,” IEEE Trans. on Information Theory, vol. 60, no. 7, pp. 4197-4231, July 2014.
• Italo Atzeni, Luis G. Ordóñez, Gesualdo Scutari, Daniel P. Palomar, and Javier R. Fonollosa, “Noncooperative Day-Ahead Bidding Strategies for Demand-Side Expected Cost Minimization with Real-Time Adjustments: A GNEP Approach,” IEEE Trans. on Signal Processing, vol. 62, no. 9, pp. 2397-2412, May 2014.
• Italo Atzeni, Luis G. Ordóñez, Gesualdo Scutari, Daniel P. Palomar, and Javier R. Fonollosa, “Demand-Side Management via Distributed Energy Generation and Storage Optimization,” IEEE Trans. on Smart Grids, vol. 4, no. 2, pp. 866-876, June 2013.
• Italo Atzeni, Luis G. Ordóñez, Gesualdo Scutari, Daniel P. Palomar, and Javier R. Fonollosa, “Noncooperative and Cooperative Optimization of Distributed Energy Generation and Storage in the Demand-Side of the Smart Grid,” IEEE Trans. on Signal Processing, vol. 61, no. 10, pp. 2454-2472, May 2013.
• Gesualdo Scutari, Daniel P. Palomar, Francisco Facchinei, and Jong-Shi Pang, “Monotone Games for Cognitive Radio Systems,” in Distributed Decision-Making and Control, Ch. 4, Eds. Anders Rantzer and Rolf Johansson, Lecture Notes in Control and Information Sciences Series, Springer Verlag, 2011. [book]
• Jong-Shi Pang, Gesualdo Scutari, Daniel P. Palomar, and Francisco Facchinei, “Design of Cognitive Radio Systems Under Temperature-Interference Constraints: A Variational Inequality Approach,” IEEE Trans. on Signal Processing, vol. 58, no. 6, pp. 3251-3271, June 2010.
• Gesualdo Scutari, Daniel P. Palomar, Francisco Facchinei, and Jong-Shi Pang, “Convex Optimization, Game Theory, and Variational Inequality Theory,” IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 35-49, May 2010.
• Gesualdo Scutari, Daniel P. Palomar, Jong-Shi Pang, and Francisco Facchinei, “Flexible Design for Cognitive Wireless Systems: From Game Theory to Variational Inequality Theory,” IEEE Signal Processing Magazine, vol. 26, no. 5, pp. 107-123, Sept. 2009.