A numerical constrained optimization method via searching for saddle points of a Lagrangian by using Artificial Bee Colony (ABC) algorithm

This paper proposes a constrained optimization method via numerically searching for saddle points of a Lagrangian. It is well-known that a solution for constrained optimization problems is equivalent to a saddle point of the corresponding Lagrangian. After developing a saddle points search method for nonlinear functions by using Artificial Bee Colony (ABC) algorithm, we propose its implementation for constrained optimization. In the proposed method, we additionary consider conditions to find non-stationary saddle points of the Lagrangian for inequality constrained problems. Numerical examples show the effectiveness of the proposed method.