Limits of SUMT Trajectories in Convex Programming

摘要

The limits of a class of primal and dual solution trajectories associated withthe Sequential Unconstrained Minimization Technique (SUMT) based on the logarithmic barrier function are investigated for convex programming problems in the presence of multiple optima and degeneracy conditions. A class of convex programming problems, identified by what is termed the 'rank-integrity property', is introduced for which primal trajectory limits can be characterized in analogy to the linear case and without differentiability conditions. This class of problems contains liner and convex quadratic programming problems as strict subsets. Similar, albeit more restricted, results are obtained for dual trajectories defined in the differentiable case.