We study the choice of the Lagrange multipliers in the successive quadratic programming method (SQP) applied to the equality constrained optimization problem.
It is known that the augmented Lagrangian SQP-Newton method depends on the penalty parameter only through the multiplier in the Hessian matrix of the Lagrangian function. This effectively reduces the augmented Lagrangian SQP-Newton method to the Lagrangian SQP Newton method where only the multiplier estimate depends on the penalty parameter. In this work, we construct a multiplier estimate that depends strongly on the penalty parameter and we derive a choice for the penalty parameter so that the Hessian matrix, restricted to the null space of the constraints, is positive definite and well conditioned. We demonstrate that the SQP-Newton method with this choice of Lagrange multipliers is locally and q-quadratically convergent.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/16725 |
| Date | January 1994 |
| Creators | Cores-Carrera, Debora |
| Contributors | Tapia, Richard A. |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 69 p., application/pdf |
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