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Title: Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

Abstract

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).

Authors:
 [1];  [1]
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  1. Northwestern Univ., Evanston, IL (United States)
Publication Date:
Research Org.:
Northwestern Univ., Evanston, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1321136
Grant/Contract Number:  
SC0005102
Resource Type:
Accepted Manuscript
Journal Name:
INFORMS Journal on Computing
Additional Journal Information:
Journal Volume: 29; Journal Issue: 1; Journal ID: ISSN 1091-9856
Publisher:
INFORMS
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; quadratic programs; quadratically constrained quadratic programs; convex programs; homogeneous algorithms; interior point methods

Citation Formats

Huang, Kuo -Ling, and Mehrotra, Sanjay. Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method. United States: N. p., 2016. Web. doi:10.1287/ijoc.2016.0715.
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Huang, Kuo -Ling, & Mehrotra, Sanjay. Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method. United States. https://doi.org/10.1287/ijoc.2016.0715
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Huang, Kuo -Ling, and Mehrotra, Sanjay. Tue . "Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method". United States. https://doi.org/10.1287/ijoc.2016.0715. https://www.osti.gov/servlets/purl/1321136.
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@article{osti_1321136,
title = {Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method},
author = {Huang, Kuo -Ling and Mehrotra, Sanjay},
abstractNote = {We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).},
doi = {10.1287/ijoc.2016.0715},
journal = {INFORMS Journal on Computing},
number = 1,
volume = 29,
place = {United States},
year = {2016},
month = {11}
}
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Works referenced in this record:

On Primal and Dual Infeasibility Certificates in a Homogeneous Model for Convex Optimization
journal, January 2000

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

On implementing a primal-dual interior-point method for conic quadratic optimization
journal, February 2003

Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
journal, December 1971

  • Bunch, J. R.; Parlett, B. N.
  • SIAM Journal on Numerical Analysis, Vol. 8, Issue 4
  • DOI: 10.1137/0708060

Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming
journal, July 2007

  • Cafieri, S.; D’Apuzzo, M.; De Simone, V.
  • Journal of Optimization Theory and Applications, Vol. 135, Issue 3
  • DOI: 10.1007/s10957-007-9264-3

On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods
journal, December 2008

  • D’Apuzzo, Marco; De Simone, Valentina; di Serafino, Daniela
  • Computational Optimization and Applications, Vol. 45, Issue 2
  • DOI: 10.1007/s10589-008-9226-1

Benchmarking optimization software with performance profiles
journal, January 2002

  • Dolan, Elizabeth D.; Moré, Jorge J.
  • Mathematical Programming, Vol. 91, Issue 2
  • DOI: 10.1007/s101070100263

MA57---a code for the solution of sparse symmetric definite and indefinite systems
journal, June 2004

Solving symmetric indefinite systems in an interior-point method for linear programming
journal, February 1993

  • Fourer, Robert; Mehrotra, Sanjay
  • Mathematical Programming, Vol. 62, Issue 1-3
  • DOI: 10.1007/BF01585158

Multiple centrality corrections in a primal-dual method for linear programming
journal, September 1996

  • Gondzio, Jacek
  • Computational Optimization and Applications, Vol. 6, Issue 2
  • DOI: 10.1007/BF00249643

An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems
journal, March 1991

  • Kojima, Masakazu; Mizuno, Shinji; Yoshise, Akiko
  • Mathematical Programming, Vol. 50, Issue 1-3
  • DOI: 10.1007/BF01594942

Conic convex programming and self-dual embedding
journal, January 2000

A repository of convex quadratic programming problems
journal, January 1999

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

Computational experience with a modified potential reduction algorithm for linear programming
journal, October 2012

Self-Scaled Barriers and Interior-Point Methods for Convex Programming
journal, February 1997

  • Nesterov, Yu. E.; Todd, M. J.
  • Mathematics of Operations Research, Vol. 22, Issue 1
  • DOI: 10.1287/moor.22.1.1

Interior-point methods for nonlinear complementarity problems
journal, March 1996

  • Potra, F. A.; Ye, Y.
  • Journal of Optimization Theory and Applications, Vol. 88, Issue 3
  • DOI: 10.1007/BF02192201

A homogeneous interior-point algorithm for nonsymmetric convex conic optimization
journal, May 2014

Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
journal, January 1999

A Centered Projective Algorithm for Linear Programming
journal, August 1990

  • Todd, Michael J.; Ye, Yinyu
  • Mathematics of Operations Research, Vol. 15, Issue 3
  • DOI: 10.1287/moor.15.3.508

Symmetric Quasidefinite Matrices
journal, February 1995

  • Vanderbei, Robert J.
  • SIAM Journal on Optimization, Vol. 5, Issue 1
  • DOI: 10.1137/0805005

A simplified homogeneous and self-dual linear programming algorithm and its implementation
journal, December 1996

  • Xu, Xiaojie; Hung, Pi-Fang; Ye, Yinyu
  • Annals of Operations Research, Vol. 62, Issue 1
  • DOI: 10.1007/BF02206815

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

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

A New Self-Dual Embedding Method for Convex Programming
journal, August 2004

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    • Petra, Cosmin G.; Potra, Florian A.
    • Computational Optimization and Applications, Vol. 72, Issue 1
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