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.

By: Frank Curtis; Johannes Huber; Olaf Schenk; Andreas Wächter

Published in: RC25143 in 2011


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to reports@us.ibm.com .