# A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

## Abstract

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

- Authors:

- Xinyang Normal University, School of Mathematics and Statistics (China)

- Publication Date:

- OSTI Identifier:
- 22769253

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; FUNCTIONS; NEWTON METHOD

### Citation Formats

```
Tang, Jingyong.
```*A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0554-6.

```
Tang, Jingyong.
```*A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs*. United States. doi:10.1007/S40314-017-0554-6.

```
Tang, Jingyong. Sun .
"A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs". United States. doi:10.1007/S40314-017-0554-6.
```

```
@article{osti_22769253,
```

title = {A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs},

author = {Tang, Jingyong},

abstractNote = {This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.},

doi = {10.1007/S40314-017-0554-6},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}