Differential-Algebraic Algorithm And Sequential Penalty Algorithm For Semidefinite Programming

This article mainly consists of two sections. In the first section, the primal semidefinite programming problem is transformed into a new problem by 'big — M' method, which is solved by differential-algebraic approach. The example given in the article demonstrates that the proposed approach provides a promising alternative for solving semidefinite programming problems. In the second section, we introduce a penalty function, then we generalize the sequential penalty algorithm for nonlinear programming problems, introduced by J. L. Zhang and X. S. Zhang, to nonlinear semidefinite programming. And under certain condition, we show that the algorithm is global convergence.