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

Journal Article · · INFORMS Journal on Computing
 [1];  [1]
  1. Northwestern Univ., Evanston, IL (United States)
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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).

Research Organization:
Northwestern Univ., Evanston, IL (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
SC0005102
OSTI ID:
1321136
Journal Information:
INFORMS Journal on Computing, Vol. 29, Issue 1; ISSN 1091-9856
Publisher:
INFORMSCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

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Cited By (1)

A homogeneous model for monotone mixed horizontal linear complementarity problems journal September 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
quadratic programs
quadratically constrained quadratic programs
convex programs
homogeneous algorithms
interior point methods