## A homogeneous model for monotone mixed horizontal linear complementarity problems

## Abstract

In this paper, we propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard linear complementarity problem. We study the properties of the model and show that interior-point methods can be used efficiently for the numerical solutions of the homogeneous problem. Finally, numerical experiments show convincingly that it is more efficient to use the proposed homogeneous model for the mixed horizontal linear complementarity problem than to use known homogeneous models for the equivalent standard linear complementarity problem.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1491659

- Report Number(s):
- LLNL-JRNL-737005

Journal ID: ISSN 0926-6003; 889808

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computational Optimization and applications

- Additional Journal Information:
- Journal Volume: 72; Journal Issue: 1; Journal ID: ISSN 0926-6003

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Mixed horizontal LCP; Homogenization; Interior-point method

### Citation Formats

```
Petra, Cosmin G., and Potra, Florian A. A homogeneous model for monotone mixed horizontal linear complementarity problems. United States: N. p., 2018.
Web. doi:10.1007/s10589-018-0035-x.
```

```
Petra, Cosmin G., & Potra, Florian A. A homogeneous model for monotone mixed horizontal linear complementarity problems. United States. doi:10.1007/s10589-018-0035-x.
```

```
Petra, Cosmin G., and Potra, Florian A. Sat .
"A homogeneous model for monotone mixed horizontal linear complementarity problems". United States. doi:10.1007/s10589-018-0035-x. https://www.osti.gov/servlets/purl/1491659.
```

```
@article{osti_1491659,
```

title = {A homogeneous model for monotone mixed horizontal linear complementarity problems},

author = {Petra, Cosmin G. and Potra, Florian A.},

abstractNote = {In this paper, we propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard linear complementarity problem. We study the properties of the model and show that interior-point methods can be used efficiently for the numerical solutions of the homogeneous problem. Finally, numerical experiments show convincingly that it is more efficient to use the proposed homogeneous model for the mixed horizontal linear complementarity problem than to use known homogeneous models for the equivalent standard linear complementarity problem.},

doi = {10.1007/s10589-018-0035-x},

journal = {Computational Optimization and applications},

number = 1,

volume = 72,

place = {United States},

year = {2018},

month = {9}

}