# Superlinear convergence of an interior-point method despite dependent constraints.

## Abstract

We show that an interior-point method for monotone variational inequalities exhibits superlinear convergence provided that all the standard assumptions hold except for the well-known assumption that the Jacobian of the active constraints has full rank at the solution. We show that superlinear convergence occurs even when the constant-rank condition on the Jacobian assumed in an earlier work does not hold.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- ER

- OSTI Identifier:
- 937949

- Report Number(s):
- MCS-P622-1196

TRN: US200905%%608

- DOE Contract Number:
- DE-AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- Math. Oper. Res.

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2 ; May 2000

- Country of Publication:
- United States

- Language:
- ENGLISH

- Subject:
- 97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONVERGENCE; JACOBIAN FUNCTION; MATHEMATICS

### Citation Formats

```
Ralph, D., Wright, S., Mathematics and Computer Science, and Univ. of Melbourne.
```*Superlinear convergence of an interior-point method despite dependent constraints.*. United States: N. p., 2000.
Web. doi:10.1287/moor.25.2.179.12227.

```
Ralph, D., Wright, S., Mathematics and Computer Science, & Univ. of Melbourne.
```*Superlinear convergence of an interior-point method despite dependent constraints.*. United States. doi:10.1287/moor.25.2.179.12227.

```
Ralph, D., Wright, S., Mathematics and Computer Science, and Univ. of Melbourne. Mon .
"Superlinear convergence of an interior-point method despite dependent constraints.". United States. doi:10.1287/moor.25.2.179.12227.
```

```
@article{osti_937949,
```

title = {Superlinear convergence of an interior-point method despite dependent constraints.},

author = {Ralph, D. and Wright, S. and Mathematics and Computer Science and Univ. of Melbourne},

abstractNote = {We show that an interior-point method for monotone variational inequalities exhibits superlinear convergence provided that all the standard assumptions hold except for the well-known assumption that the Jacobian of the active constraints has full rank at the solution. We show that superlinear convergence occurs even when the constant-rank condition on the Jacobian assumed in an earlier work does not hold.},

doi = {10.1287/moor.25.2.179.12227},

journal = {Math. Oper. Res.},

number = 2 ; May 2000,

volume = 25,

place = {United States},

year = {2000},

month = {5}

}

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