### ICASSP: Game theory

Before enjoying the amazing rodeo at the ICASSP yesterday I catched two interesting results on game theory (field in which I also carried out some research) that I comment next. On the other hand it looks that today is the day on compressed sampling, since most of the talks are on this topic. I will comment some of these results in a future post.

The paper

Stephen P. Boyd once said in his lecture 364A that we cannot state that problems are convex only because exists a transformation that maps the original problem into an equivalent convex formulation. This definition would imply that we could never say that a given problem is non-convex, since it may exists an unknown transformation such that there exists a convex formulation.

The work

The paper

**DESIGN OF COGNITIVE RADIO SYSTEMS UNDER TEMPERATURE-INTERFERENCE CONSTRAINTS: A VARIATIONAL INEQUALITY APPROACH**by Jong-Shi Pang et al. presents a novel approach to simultaneous waterfilling in a cognitive scenario where secondary users have to maximize their own transmission rate and simultaneously satisfy the interference constraint imposed by the primary user. In a nice presentation D. P. Palomar explained how this problem can be addressed by translating the interference constraints into the maximization problem through lagrange multipliers. I was surprised that a similar strategy was used by J. A. Bazerque in his approach to the distributed Lasso, what indicates that this approach is useful for deriving distributed version of algorithms with global constraints.Stephen P. Boyd once said in his lecture 364A that we cannot state that problems are convex only because exists a transformation that maps the original problem into an equivalent convex formulation. This definition would imply that we could never say that a given problem is non-convex, since it may exists an unknown transformation such that there exists a convex formulation.

The work

**CONCAVE RESOURCE ALLOCATION PROBLEMS FOR INTERFERENCE COUPLED WIRELESS SYSTEMS**by Holger Boche et al. studies this problem for practical functions of the SINR that is neither convex or concave on the set of powers.The paper shows that there exists no transformation (given a set of constraints on the allowed transformations) that ensures concavity for all linear interference functions for all functions of SINR. Then it shows that for an exponential transformation on the powers this concavity is achieved for a class of utility functions. I need to take a closer look to the paper, but it looks quite interesting for practical SINR-based power control algorithms.Labels: game theory, icassp 2010

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