Abstract
A trust region method for nonlinear optimization problems with equality constraints is proposed in this paper. This method incorporates quadratic subproblems in which orthogonal projective matrices of the Jacobian of constraint functions are used to replace QR decompositions. As QR decomposition does not ensure continuity, but projective matrix does, convergence behaviour of the new method can be discussed under more reasonable assumptions. The method maintains a two-step feature: one movement in the range space of the Jacobian, whereas the other one in the null space. It is proved that all accumulation points of iterates are KKT (Karush-Kuhn-Tucker) points and the method has a one-step superlinear convergence rate. © 1994.
| Original language | English |
|---|---|
| Pages (from-to) | 291-307 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 53 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 30 Aug 1994 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
Partially supported by the City Polytechnic of Hong Kong (Research Grant 700126).
Research Keywords
- Nonlinear optimization
- Projective matrix
- Quasi-Newton method
- Trust region method
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