A Filter Line-search Interior Point Method For Nonlinear Constrained Optimization Problem

The filter line-search method has been widely studied for years, and this method is very valuable and meaningful when we deal with nonlinear constrained optimization problems. The line search-filter method presented with an interior point framework is an important way to study the nonlinear constrained optimization problems. This method converts a problem into a series of barrier problems, and then we just solve those barriers problems by filter line-searching and second-order corrections.In this paper, we present an interior-point algorithm with a filter line-search method for nonlinear programming, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. It is shown that this approach has global convergence properties under certain conditions. Numerical results show that it is suitable for nonlinear constrained problems and has good numerical stability.