Several Smoothing Methods For Exact Penalty Functions

Constrained optimization is an important subject in nonlinear programming. Inchapter1, we review the research status of exact penalty functions. In chapter2, wepropose a second-order smoothing method to lower order exact penalty functions forinequality constrained optimization problems. An algorithm is designed to obtain anapproximate optimal solution of the original problem by finding a optimal solution ofthe smoothed penalty problem. Numerical examples are given to show the effectivenessof the present smoothing method. In chapter3, we propose a second-order smoothingmethod to the square-root exact penalty function for inequality constrained optimizationproblem. Error estimations are obtained among the optimal objective function values ofthe smoothed penalty problem, of the penalty problem and of the original optimizationproblem. We design an algorithm for solving the original problem based on thesmoothed penalty function and prove the convergence of the algorithm. An exampleshow that the algorithm presented in the chapter is efficient. effectiveness of the presentsmoothing method. In chapter4, we give a new exact penalty function for equalityconstrained optimization problem and discuss some theoretical properties of thefunction under suitable constraint qualifications.