Abstract
Although variable metric methods for constrained minimization generally give good numerical results, many of their convergence properties are still open. In this note two examples are presented to show that variable metric methods may cycle between two points instead of converging to the required solution.
This is a preview of subscription content, log in via an institution to check access.
References
R. Fletcher, “An algorithm for solving linearly constrained optimization problems”,Mathematical Programming 2 (1972) 133–165.
U.M. Garcia Palomares and O.L. Mangasarian, “Superlinearly convergent quasi-Newton algorithms for nonlinearly constrained optimization problems”,Mathematical Programming 11 (1976) 1–13.
S.P. Han, “Superlinearly convergent variable metric algorithms for general nonlinear programming problems”,Mathematical Programming 11 (1976) 263–282.
S.P. Han, “A globally convergent method for nonlinear programming”,Journal of Optimization Theory and Applications 22 (1977) 297–309.
M.J.D. Powell, “Algorithms for nonlinear constraints that use Lagrangian functions”,Mathematical Programming 14 (1978) 224–248.
M.J.D. Powell, “A fast algorithm for nonlinearly constrained optimization calculations”, in: G.A. Watson, ed.,Numerical analysis, Dundee 1977, Lecture Notes in Mathematics, No. 630 (Springer, Berlin, 1978) pp. 144–157.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chamberlain, R.M. Some examples of cycling in variable metric methods for constrained minimization. Mathematical Programming 16, 378–383 (1979). https://doi.org/10.1007/BF01582123
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01582123