Degenerate nonlinear programming with a quadratic growth condition.
We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- SC
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 942679
- Report Number(s):
- ANL/MCS-P761-0699
- Journal Information:
- SIAM J. Optimization, Journal Name: SIAM J. Optimization Journal Issue: 4 ; 2000 Vol. 10; ISSN 1052-6234
- Country of Publication:
- United States
- Language:
- ENGLISH
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