A Primal-Dual Interior-Point Method Of Using The Augmented Lagrangian Function For Nonlinear Semidefinite Programming

We consider a primal-dual interior point method for solving nonlinear semi-definite programming problems. We take a augmented lagrangian function as themerit function, The penalty parameterβin the merit function plays two roles in themethod: First, it guarantees that the search directions obtained by the Armijo ruleare descent directions; Second, it helps to in?uence the regularization parameterλ_d of the Karush-Kuhn-Tucker system of the barrier subproblem by iterating. Lettheλ_d be reciprocal of theβ, when theβbecomes big enough, theλ_d becomessmall enough, then it guarantees that every limit point of the sequence generatedby the method is a Karush-Kuhn-Tucker point of the primal problems.