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A Note on the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations

Frank E. Curtis (frank.e.curtis***at***lehigh.edu)
Johannes Huber (johannes.huber***at***unibas.ch)
Olaf Schenk (olaf.schenk***at***usi.ch)
Andreas Wächter (waechter***at***iems.northwestern.edu)

Abstract: This paper describes an implementation of an interior-point algorithm for large-scale nonlinear optimization. It is based on the algorithm proposed by Curtis et al. (SIAM J Sci Comput 32:3447–3475, 2010), 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. The implementation follows the proposed algorithm, but includes many practical enhancements, such as functionality to avoid the computation of a normal step during every iteration. The implementation is included in the IPOPT software package paired with an iterative linear system solver and preconditioner provided in PARDISO. 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.

Keywords: large-scale optimization, PDE-constrained optimization, interior- point methods, nonconvex programming, line search, trust regions, inexact linear system solvers, Krylov subspace methods

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: F. E. Curtis, J. Huber, O. Schenk, and A.W¨achter, “A Note on the Implementation of an Interior-Point Algorithm for Nonlinear Optimization with Inexact Step Computations,” Mathematical Programming Series B, 32(6): 3447–3475, 2012.

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Entry Submitted: 04/15/2011
Entry Accepted: 04/15/2011
Entry Last Modified: 05/31/2014

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