The Study On Several Algorithms For Semidefinite Programming

Several algorithms for semidefinite programming are studied, which include the contraction mapping algorithm and predictor-corrector algorithm.Firstly, the basics knowledge of SDP is introduced. These include the standard semidefinite programming, semidefinite programming duality theory, two main algorithms for semidefinite programming: interior point method and the spectral bundle algorithm, and then simply give the applications in the second optimization for the cone and quadratic programming.Then, a predictor-corrector algorithm for a sub-class of semidefinite programming problem is proposed with the exsited theroy in the path following algorithm, and through numerical experiments the proposed algorithm is tested.At last, with the help of the equivalent between semidefinite programming and a subclass of variational inequality and the equivalent between this variational inequality and projection mapping algorithm, projection mapping algorithm is used for solving semidefinite programming. Thus a circuit is proposed basing on the mapping algorithm, at the same time, the stability of the mapping algorithm and evolutionary convergence are proved theoretically too.