Constructing a continuously differentiable exact augmented Lagrangian function for nonlinear semidefinite programming (The state-of-the-art optimization technique and future development)

Abstract

In this note, we will construct a continuouly differentiable exact augmented Lagrangian function for nonlinear semidefinite programming problems. This function is defined on the product space of the problem s variables and of the multipliers. The unconstrained minimization of the proposed exact augmented Lagrangian gives a solution of the original problem, when the penalty parameter is large enough. We will show that the exactness property holds when the nondegeneracy condition is assumed.