Primal–dual Newton method with steepest descent for the linear semidefinite programming problem: Newton's system of equations

The linear semidefinite programming problem is considered. It is proposed to solve it using a feasible primal–dual method based on solving the system of equations describing the optimality conditions in the problem by Newton’s method. The selection of Newton’s displacement directions in the case when the current points of the iterative process lie on the boundaries of feasible sets is discussed. The partition of the space of symmetric matrices into subspaces is essentially used.