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 interiorpoint 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)
 OSTI Identifier:
 1491659
 Report Number(s):
 LLNLJRNL737005
Journal ID: ISSN 09266003; 889808
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computational Optimization and Applications
 Additional Journal Information:
 Journal Volume: 72; Journal Issue: 1; Journal ID: ISSN 09266003
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mixed horizontal LCP; Homogenization; Interiorpoint 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/s105890180035x.
Petra, Cosmin G., & Potra, Florian A.. A homogeneous model for monotone mixed horizontal linear complementarity problems. United States. https://doi.org/10.1007/s105890180035x
Petra, Cosmin G., and Potra, Florian A.. Sat .
"A homogeneous model for monotone mixed horizontal linear complementarity problems". United States. https://doi.org/10.1007/s105890180035x. 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 interiorpoint 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/s105890180035x},
journal = {Computational Optimization and Applications},
number = 1,
volume = 72,
place = {United States},
year = {2018},
month = {9}
}
Web of Science
Figures / Tables:
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