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Degenerate Nonlinear Programming with a Quadratic Growth Condition (0)
| Venue: | Preprint ANL/MCS-P761-0699, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill |
| Citations: | 18 - 5 self |
BibTeX
@ARTICLE{Anitescu_degeneratenonlinear,
author = {Mihai Anitescu},
title = {Degenerate Nonlinear Programming with a Quadratic Growth Condition},
journal = {Preprint ANL/MCS-P761-0699, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill},
year = {},
volume = {10},
pages = {1116--1135}
}
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Abstract
. We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification 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 Mangasarian-Fromovitz constraint qualification 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. 1. Introduction. Recently, there has been renewed interest in analyzing and modifying sequential quadratic programming (SQP) algorithms for constrained nonlinear optimization for cases where the traditional regularity cond...
Keyphrases
quadratic growth condition degenerate nonlinear local minimum mangasarian-fromovitz constraint qualification imply quadratic growth stationary point nonlinear optimization positive semidefinite mangasarian-fromovitz constraint qualification degenerate nonlinear program traditional regularity cond sequential quadratic programming present numerical result r-linear convergence unique local minimum several nonlinear programming package lagrangian exists nonlinear program
