# A New Noninterior Predictor-Corrector Method for the P{sub 0} LCP

## Abstract

In this paper a new predictor-corrector noninterior method for LCP is presented, in which the predictor step is generated by the Levenberg-Marquadt method, which is new in the predictor-corrector-type methods, and the corrector step is generated as in [3]. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P{sub 0} LCP; (ii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P{sub 0} LCP superlinearly; (iii) for the P{sub 0} LCP, if an accumulation point of the iteration sequence satisfies the strict complementary condition, then the whole sequence converges to this accumulation point superlinearly. Preliminary numerical experiments are reported to show the efficiency of the algorithm.

- Authors:

- Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Graduate University of the Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100080 (China), E-mail: jlzhang@gucas.ac.cn
- Department of Management Science and Engineering, School of Economics and Management, Tsinghua University, Beijing 100084 (China)

- Publication Date:

- OSTI Identifier:
- 21067428

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 53; Journal Issue: 1; Other Information: DOI: 10.1007/s00245-005-0836-z; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ITERATIVE METHODS; JACOBIAN FUNCTION; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Zhang Juliang, and Chen Jian.
```*A New Noninterior Predictor-Corrector Method for the P{sub 0} LCP*. United States: N. p., 2006.
Web. doi:10.1007/S00245-005-0836-Z.

```
Zhang Juliang, & Chen Jian.
```*A New Noninterior Predictor-Corrector Method for the P{sub 0} LCP*. United States. doi:10.1007/S00245-005-0836-Z.

```
Zhang Juliang, and Chen Jian. Sun .
"A New Noninterior Predictor-Corrector Method for the P{sub 0} LCP". United States.
doi:10.1007/S00245-005-0836-Z.
```

```
@article{osti_21067428,
```

title = {A New Noninterior Predictor-Corrector Method for the P{sub 0} LCP},

author = {Zhang Juliang and Chen Jian},

abstractNote = {In this paper a new predictor-corrector noninterior method for LCP is presented, in which the predictor step is generated by the Levenberg-Marquadt method, which is new in the predictor-corrector-type methods, and the corrector step is generated as in [3]. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P{sub 0} LCP; (ii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P{sub 0} LCP superlinearly; (iii) for the P{sub 0} LCP, if an accumulation point of the iteration sequence satisfies the strict complementary condition, then the whole sequence converges to this accumulation point superlinearly. Preliminary numerical experiments are reported to show the efficiency of the algorithm.},

doi = {10.1007/S00245-005-0836-Z},

journal = {Applied Mathematics and Optimization},

number = 1,

volume = 53,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}