  In this paper, we propose a new nonlinear optimization model to solve
semidefinite optimization problems (SDPs), providing some properties related to
local optimal solutions. The proposed model is based on another nonlinear
optimization model given by Burer and Monteiro (2003), but it has several nice
properties not seen in the existing one. Firstly, the decision variable of the
proposed model is a triangular low-rank matrix, and hence the dimension of its
decision variable space is smaller. Secondly, the existence of a strict local
optimum of the proposed model is guaranteed under some conditions, whereas the
existing model has no strict local optimum. In other words, it is difficult to
construct solution methods equipped with fast convergence using the existing
model. Some numerical results are also presented to examine the efficiency of
the proposed model.
