We present a new algorithm for nonlinear semide nite programming. It is based on the iterative solution, in the primal and dual variables, of Karush- Kuhn-Tucker rst order optimality conditions. This method generates a decreasing feasible sequence. At each iteration, two linear systems with the same coe cient matrix are solved and an inexact line search is then performed. A proof of global convergence is given in the convex case. Some numerical tests involving nonlin- ear programming problems as well linear and nonlinear matrix inequalities are described. We also solve structural topology optimization problems employing a mathematical model based on semide nite programming. The results suggest e - ciency and high robustness of the proposed method.
