Title
A Matrix-Free Trust-Region SQP Method for Equality Constrained Optimization.
Abstract
We develop and analyze a trust-region sequential quadratic programming (SQP) method for the solution of smooth equality constrained optimization problems, which allows the inexact and hence iterative solution of linear systems. Iterative solution of linear systems is important in large-scale applications, such as optimization problems with partial differential equation constraints, where direct solves are either too expensive or not applicable. Our trust-region SQP algorithm is based on a composite-step approach that decouples the step into a quasi-normal and a tangential step. The algorithm includes critical modifications of substep computations needed to cope with the inexact solution of linear systems. The global convergence of our algorithm is guaranteed under rather general conditions on the substeps. We propose algorithms to compute the substeps and prove that these algorithms satisfy global convergence conditions. All components of the resulting algorithm are specified in such a way that they can be directly implemented. Numerical results indicate that our algorithm converges even for very coarse linear system solves.
Year
DOI
Venue
2014
10.1137/130921738
SIAM JOURNAL ON OPTIMIZATION
Keywords
DocType
Volume
sequential quadratic programming,trust-region,large-scale optimization,matrix free,inexact linear system solvers,PDE-constrained optimization,Krylov subspace methods
Journal
24
Issue
ISSN
Citations 
3
1052-6234
1
PageRank 
References 
Authors
0.37
0
2
Name
Order
Citations
PageRank
Matthias Heinkenschloss110.37
Denis Ridzal2759.99