Algorithm of Barrier Objective Penalty Function

In this paper, an algorithm of barrier objective penalty function for inequality constrained optimization is studied and a conception–the stability of barrier objective penalty function is presented. It is proved that an approximate optimal solution may be obtained by solving a barrier objective penalty function for inequality constrained optimization problem when the barrier objective penalty function is stable. Under some conditions, the stability of barrier objective penalty function is proved for convex programming. Specially, the logarithmic barrier function of convex programming is stable. Based on the barrier objective penalty function, an algorithm is developed for finding an approximate optimal solution to an inequality constrained optimization problem and its convergence is also proved under some conditions. Finally, numerical experiments show that the barrier objective penalty function algorithm has better convergence than the classical barrier function algorithm.