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Title: 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:
ORCiD logo [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. 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):
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Table 1 Table 1: Solvability and infeasibility certificates given by $τ$ and $κ$

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Works referenced in this record:

On a homogeneous algorithm for the monotone complementarity problem
journal, February 1999


Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones
journal, January 2007

  • Yoshise, Akiko
  • SIAM Journal on Optimization, Vol. 17, Issue 4
  • DOI: 10.1137/04061427X

On the Implementation of a Primal-Dual Interior Point Method
journal, November 1992

  • Mehrotra, Sanjay
  • SIAM Journal on Optimization, Vol. 2, Issue 4
  • DOI: 10.1137/0802028

On homogeneous and self-dual algorithms for LCP
journal, January 1997


A new polynomial-time algorithm for linear programming
journal, December 1984


On interior algorithms for linear programming with no regularity assumptions
journal, May 1992


Generalized Linear Complementarity Problems
journal, May 1995


Convergence of Interior Point Algorithms for the Monotone Linear Complementarity Problem
journal, February 1996

  • Bonnans, J. Frédéric; Gonzaga, Clovis C.
  • Mathematics of Operations Research, Vol. 21, Issue 1
  • DOI: 10.1287/moor.21.1.1

Properties of an Interior-Point Mapping for Mixed Complementarity Problems
journal, August 1996

  • Monteiro, R. D. C.; Pang, Jong-Shi
  • Mathematics of Operations Research, Vol. 21, Issue 3
  • DOI: 10.1287/moor.21.3.629

Equivaence between different formulations of the linear complementarity promblem
journal, January 1997

  • anitescu, Mihai; Lesaja, Goran; Potra, Florian A.
  • Optimization Methods and Software, Vol. 7, Issue 3-4
  • DOI: 10.1080/10556789708805657

Object-oriented software for quadratic programming
journal, March 2003

  • Gertz, E. Michael; Wright, Stephen J.
  • ACM Transactions on Mathematical Software, Vol. 29, Issue 1
  • DOI: 10.1145/641876.641880

HOPDM (version 2.12) — A fast LP solver based on a primal-dual interior point method
journal, August 1995


An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm
journal, February 1994

  • Ye, Yinyu; Todd, Michael J.; Mizuno, Shinji
  • Mathematics of Operations Research, Vol. 19, Issue 1
  • DOI: 10.1287/moor.19.1.53

Generalizations of P0- and P-properties; extended vertical and horizontal linear complementarity problems
journal, July 1995


Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method
journal, January 2017

  • Huang, Kuo-Ling; Mehrotra, Sanjay
  • INFORMS Journal on Computing, Vol. 29, Issue 1
  • DOI: 10.1287/ijoc.2016.0715

On Implementing Mehrotra’s Predictor–Corrector Interior-Point Method for Linear Programming
journal, August 1992

  • Lustig, Irvin J.; Marsten, Roy E.; Shanno, David F.
  • SIAM Journal on Optimization, Vol. 2, Issue 3
  • DOI: 10.1137/0802022

A Mehrotra-type predictor-corrector algorithm with polynomiality andQ-subquadratic convergence
journal, December 1996

  • Zhang, Detong; Zhang, Yin
  • Annals of Operations Research, Vol. 62, Issue 1
  • DOI: 10.1007/BF02206814

Reducing a monotone horizontal LCP to an LCP
journal, January 1995


On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems
journal, February 1998

  • Monteiro, R. D. C.; Pang, Jong-Shi
  • Mathematics of Operations Research, Vol. 23, Issue 1
  • DOI: 10.1287/moor.23.1.39

A new polynomial-time algorithm for linear programming
conference, January 1984

  • Karmarkar, N.
  • Proceedings of the sixteenth annual ACM symposium on Theory of computing - STOC '84
  • DOI: 10.1145/800057.808695

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.