Abstract: In this paper, we introduce a nonsmoothed square-root penalty function for nonlinear constrained optimization. We propose a smoothing function for the nonsmooth penalty function and define the corresponding smoothed penalty problem and obtain some error estimations among their optimal objective function values for the smoothed penalty problem and the original optimization problem. We develop an algorithm based on the smoothed penalty function and prove the convergence of the algorithm. Numerical examples show that the proposed algorithm is efficient for solving some nonlinear constrained optimization problems.

Key words: nonlinear constrained optimization, square-root penalty function, exactness, smooth