existence of trajectory – Optimization Online

Interior Point Trajectories and a Homogeneous Model for Nonlinear Complementarity Problems over Symmetric Cones

Published: 2004/08/09, Updated: 2007/01/16

Complementarity and Variational Inequalities, Linear, Cone and Semidefinite Programming complementarity problem, detecting infeasibility, existence of trajectory, homogeneous algorithm, interior point methods, symmetric cones

We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in Faybusovich (1997) depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang (1998), where a vast set of conclusions concerning continuous trajectories is shown for monotone … Read more

A Homogeneous Model for $ and *$ Nonlinear Complementarity Problems

Published: 2003/09/30, Updated: 2011/11/07

Akiko Yoshise

Complementarity and Variational Inequalities $ and *$ complementarity problem, existence of trajectory, global convergence, homogeneous algorithm

The homogeneous model for linear programs is an elegant means of obtaining the solution or certificate of infeasibility and has importance regardless of the method used for solving the problem, interior-point methods or other methods. In 1999, Andersen and Ye generalized this model to monotone complementarity problems (CPs) and showed that most of the desirable … Read more