Abstract: In this paper, we consider the positive semidefinite solution to a class of generalized Lyapunov matrix equation, which arises in bilinear systems. Based on the good property that the local minimizer of a convex function is also the global minimizer, the positive semidefinite solution of the generalized Lyapunov equation is transformed into a convex optimization problem. By using the nonmonotone line search technique, we develop a nonmonotone spectral projected gradient method to solve this equivalent problem. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the new method.

Key words: generalized Lyapunov equation, positive semidefinite solution, nonmonotone line search, projected gradient method