On the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations

This paper describes a practical implementation of a line-search interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis, Schenk, and Wächter [SIAM J. Sci. Comput., 32 (2010), pp. 3447-3475], a method that possesses global convergence guarantees to first-order stationary points with the novel feature that inexact search direction calculations are allowed in order to save computational expense during each iteration. The implementation follows the proposed algorithm, except that additional functionality is included to avoid the explicit computation of a normal step during every iteration. It also contains further enhancements that have not been studied along with the previous theoretical analysis. The implementation has been included in the IPOPT software package paired with an iterative linear system solver and preconditioner provided in the PARDISO software. Numerical results on a large nonlinear optimization test set and two PDE-constrained optimization problems with control and state constraints are presented to illustrate that the implementation is robust and efficient for large-scale applications.