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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]
  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) (SC-21)
OSTI Identifier:
1321136
Grant/Contract Number:
SC0005102
Resource Type:
Journal Article: 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.
Huang, Kuo -Ling, & Mehrotra, Sanjay. Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method. United States. doi:10.1287/ijoc.2016.0715.
Huang, Kuo -Ling, and Mehrotra, Sanjay. 2016. "Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method". United States. doi:10.1287/ijoc.2016.0715. https://www.osti.gov/servlets/purl/1321136.
@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 =
}

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