Abstract
In this paper we discuss the application of the stabilized SQP method with constraint identification (sSQPa) recently proposed by S. J. Wright 12 for nonlinear programming problems at which strict complementarity and/or linear independence of the gradients of the active constraints may fail to hold at the solution. We have collected a number of degenerate problems from different sources. Our numerical experiments have shown that the sSQPa is efficient and robust even without the incorporation of a classical globalization technique. One of our goals is therefore to handle NLPs that arise as subproblems in global optimization where degeneracy and infeasibility are important issues. We also discuss and present our work along this direction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Anitescu, M.: Degenerate nonlinear programming with a quadratic growth condition. SIAM J. Optim. 10, 1116–1135 (2000)
Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9, 14–32 (1998)
Hager, W.W.: Stabilized sequential quadratic programming. Comput. Optim. and Appl. 12, 253–273 (1999)
Heinkenschloss, M., Ulbrich, M., Ulbrich, S.: Superlinear and quadratic convergence of affine-scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption. Math. Programming 86, 615–635 (1999)
Hock, W., Schittkowski, K.: Test examples for nonlinear programming codes. Lecture Notes in Economics and Math. Systems, vol. 187. Springer, Berlin (1981)
Li, D.-H., Qi, L.: A stabilized SQP method via linear equations, Technical report, Mathematics Department, University of New South Wales (2000)
de Miguel, V., Murray, W.: Generating optimization problems with global variables, Technical Report TR/SOL 01–3, Management Science & Eng., Stanford Univ. (2001)
Ralph, D., Wright, S.J.: Superlinear convergence of an interior-point method despite dependent constraints. Math. Oper. Res. 25, 179–194 (2000)
Vicente, L.N., Wright, S.J.: Local convergence of a primal–dual method for degenerate nonlinear programming, Department of Mathematics, University of Coimbra (2000) (revised May 2001) (preprint 00–05)
Wright, S.J.: Modifying SQP for degenerate problems, Preprint ANL/MCS– P699-1097, Argonne National Laboratory (1998) (revised June 2000)
Wright, S.J.: Superlinear convergence of a stabilized SQP method to a degenerate solution. Comput. Optim. and Appl. 11, 253–275 (1998)
Wright, S.J.: Constraint identification and algorithm stabilization for degenerate nonlinear programs, Argonne National Laboratory, 2000 (revised November 2001) (preprint ANL/MCS–P865-1200)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mostafa, E.M.E., Vicente, L.N., Wright, S.J. (2003). Numerical Behavior of a Stabilized SQP Method for Degenerate NLP Problems. In: Bliek, C., Jermann, C., Neumaier, A. (eds) Global Optimization and Constraint Satisfaction. COCOS 2002. Lecture Notes in Computer Science, vol 2861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39901-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-39901-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20463-3
Online ISBN: 978-3-540-39901-8
eBook Packages: Springer Book Archive