Abstract
In this paper we give examples illustrating the behavior of the Coleman-Conn horizontal vertical method and of successive quadratic programming with a Hessian approximation exact on the tangent space of the constraints. One example shows that these methods in general are not one-step superlinearly convergent.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P.T. Boggs, J.W. Tolle and P. Wang, “On the local convergence of quasi-Newton methods for constrained optimization”,SIAM Journal on Control and Optimization 20 (1982), 161–171.
T.F. Coleman and A.R. Conn, “Nonlinear programming via an exact penalty function method: asymptotic analysis”,Mathematical Programming 24 (1982), 123–136.
T.F. Coleman and A.R. Conn, “On the local convergence of a quasi-Newton method for a nonlinear programming problem”, Technical Report 82-509, Department of Computer Science, Cornell University (Ithaca, NY, 1982).
R. Fontecilla, T. Steihaug and R. Tapia, “A convergence theory for a class of quasi-Newton methods for constrained optimization”, Technical Report 83-15, Department of Mathematical Sciences, Rice University (Houston, 1983).
M.J.D. Powell, “The convergence of variable metric methods for nonlinearly constrained optimization calculations”, in: O. Mangasarian, R. Meyer and S. Robinson, eds.,Nonlinear Programming 3 (Academic Press, New York, 1978) pp. 27–63.
Y. Yuan, “On the reduced Hessian method for constrained optimization”, Technical Report DAMTP 1984/NA1, Department of Applied Mathematics and Theoretical Physics, Cambridge University (Cambridge, England, 1984).
Author information
Authors and Affiliations
Additional information
This research was supported by National Science Foundation Grant MCS-8115475.
Rights and permissions
About this article
Cite this article
Byrd, R.H. An example of irregular convergence in some constrained optimization methods that use the projected hessian. Mathematical Programming 32, 232–237 (1985). https://doi.org/10.1007/BF01586093
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01586093