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 is satis ed. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear polynomial-time convergence properties while achieving practical performance. When compared with a 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.
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Address: Dept. of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 60208 Email: mehrotra@iems.northwestern.edu