Monotone operators and local-global minimum property of nonlinear optimization problems

Abstract. Our main goal is to prove that every local minimizer of a certain nonlinear optimization problem is global. For this, we use some results from the theory of monotone operators and connected functions. At last, we show applications of the main results in control theory.

Key words and phrases. Local-global minimum poroperty, monotone operators, nonlinear optimization, nonconvex optimization.