2010 (English)Report (Other academic)
In wireless sensors networks it is common that decision variables must be optimized by algorithms that need tobe fast, simple, and robust to errors and noises, both in a centralized and in a distributed set-up. A new simple vectoroptimization theory, named the fast Lipschitz (F-Lipschitz) optimization, is introduced for a novel class of nonlinearmulti-objective optimization problems that are pervasive in wireless sensor networks. These problems are deﬁnedby qualifying properties speciﬁed in terms of increasing objective function and partially monotonic constraints. It isshown that feasible F-Lipschitz problems have always a unique Pareto optimal solution that satisﬁes all the constraintsat the equality, including the inequality constraints. The solution is obtained quickly by asynchronous algorithmsof certiﬁed convergence. F-Lipschitz optimization can be applied to both centralized and distributed optimization.Compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralizedF-Lipschitz algorithms is superlinear. Distributed F-Lipschitz algorithms converge fast, as opposed to traditionalLagrangian decomposition and parallelization methods, which generally converge slowly and at the price of manymessage passings. In both cases, the computational complexity is much lower than traditional Lagrangian methods.It is shown that the interference function theory, which plays a central role in distributed resource allocation ofwireless communication systems, is a particular case of F-Lipschitz optimization. It is proved that a class of convexproblems, including geometric programming problems, can be cast as F-Lipschitz problems, and thus they can besolved much more efﬁciently than interior point methods. Some typical optimization problems that occur on wirelesssensor networks are shown to be F-Lipschitz. For more general optimization problems, it is suggested that beforesolving them by Lagrangian methods, it is convenient having conditions ensuring that the solution satisﬁes part or allof the constraints at the equality. The drawback of the F-Lipschitz optimization is that it might be difﬁcult to checkthe qualifying properties.
Place, publisher, year, edition, pages
2010. , 34 p.
, IR-EE-RT, 2010:023
Interference Function Theory, Convex and Non-convex Optimization, Parallel and Distributed Computation, Distributed Optimization, Geometric Programming, Wireless Sensor Networks
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-124017OAI: oai:DiVA.org:kth-124017DiVA: diva2:632276
QC 201306252013-06-242013-06-242013-06-25Bibliographically approved