Semidefinite Programming And Its Application In Wireless Sensor Network Localization

Semidefinite programming is an extension of linear programming. withvector variables replaced by matrix variables and non-negativity elementwisereplaced by positive semidefiniteness. In linear semidefinite programming onemaximizes (minimizes) a linear function subject to the constraint that an a?necombination of symmetric matrices is positive semidefinite. Such a constraint isnonlinear and nonsmooth, but convex, so linear semidefinite programs are nons-mooth convex optimization problems. several classical optimization problems canbe formulated as standard semidefinite programming. Therefore semidefinite pro-gramming provides a unit form to study these problems and construct algorithms,and its most important applications are found in control theory, combinatorialoptimization, system engineering and eigenvalue optimization.In the paper, we summarize the theory, algorithm, and recent research ofsemidefinite programming, then, introduce our work in theory ,algorithm andsensor network localization. We conclude them as follows:1. Based on the equivalently transforming the optimality conditions of thesemidefinite programming as an equivalent nonlinear system of equations,but wecan not solve it exactly,so we can solve it approximately ,a Newton algorithmfor semidefinite programming is proposed,and it is showed that the algorithmcan find anγ-approximate solution for an SDP problem. And we analysis itsconvergence.2.In wireless sensor network,it is very important for its node localization,Severalsemidefinite programming relaxation models are presented to get the approximatesolution for wireless sensor network localization. Combining numerical experi-ments, the advantages and the disadvantages of them are analyzed.