Orizon Pereira Ferreira In this paper we consider the proximal point method with Bregman distance applied to linear programming problems, and study the dual sequence obtained from the optimal multipliers of the linear constraints of each subproblem. We establish the convergence of this dual sequence, as well as convergence rate results for the primal sequence, for a suitable … Read more
The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more
This paper studies the asymptotic behavior of the central path $(X(\nu),S(\nu),y(\nu))$ as $\nu \downarrow 0$ for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” $X_{\cT}(\nu)$ and $S_{\cT}(\nu)$ of the central path are assumed to satisfy $\max\{ \|X_{\cT}(\nu)\|, \|S_{\cT}(\nu)\| \} … Read more