Multiplier Algorithm Based on A New Augmented Lagrangian Function

In this paper, for nonconvex optimization problem with both equality and inequality constrains, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. The global convergence is established without requiring the boundedness of multiplier sequences. In particular, if the algorithm terminates in finite steps, then we obtain a KKT point of the primal problem; otherwise the iterative sequence {xk} generalized by algorithm converges to optimal solutions. Even if {xk} is divergent we also present a necessary and sufficient condition for the convergence of {f(xk)} to the optimal value. Finally, preliminary numerical experience is reported. Key–Words: constrained global optimization, multiplier algorithm, global convergence