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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];  [2]
  1. Northwestern Univ., Evanston, IL (United States); Northwestern University
  2. Northwestern Univ., Evanston, IL (United States)
+ Show Author Affiliations

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) (SC-21)
Grant/Contract Number:
SC0005102
OSTI ID:
1321136
Journal Information:
INFORMS Journal on Computing, Journal Name: INFORMS Journal on Computing Journal Issue: 1 Vol. 29; ISSN 1091-9856
Publisher:
INFORMSCopyright Statement
Country of Publication:
United States
Language:
English

References (25)

Multiple centrality corrections in a primal-dual method for linear programming journal September 1996
Solving symmetric indefinite systems in an interior-point method for linear programming journal February 1993
An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems journal March 1991
Interior-point methods for nonlinear complementarity problems journal March 1996
A simplified homogeneous and self-dual linear programming algorithm and its implementation journal December 1996
On implementing a primal-dual interior-point method for conic quadratic optimization journal February 2003
A homogeneous interior-point algorithm for nonsymmetric convex conic optimization journal May 2014
On a homogeneous algorithm for the monotone complementarity problem journal February 1999
Benchmarking optimization software with performance profiles journal January 2002
On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods journal December 2008
Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming journal July 2007
A New Self-Dual Embedding Method for Convex Programming journal August 2004
Conic convex programming and self-dual embedding journal January 2000
Computational experience with a modified potential reduction algorithm for linear programming journal October 2012
Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones journal January 1999
A repository of convex quadratic programming problems journal January 1999
Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones journal January 2007
Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations journal December 1971
On the Implementation of a Primal-Dual Interior Point Method journal November 1992
Symmetric Quasidefinite Matrices journal February 1995
On Primal and Dual Infeasibility Certificates in a Homogeneous Model for Convex Optimization journal January 2000
MA57---a code for the solution of sparse symmetric definite and indefinite systems journal June 2004
A Centered Projective Algorithm for Linear Programming journal August 1990
An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm journal February 1994
Self-Scaled Barriers and Interior-Point Methods for Convex Programming journal February 1997

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
convex programs
homogeneous algorithms
interior point methods
quadratic programs
quadratically constrained quadratic programs