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Displaying similar documents to “On the central paths and Cauchy trajectories in semidefinite programming”

A new barrier for a class of semidefinite problems

Erik A. Papa Quiroz, Paolo Roberto Oliveira (2006)

RAIRO - Operations Research

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We introduce a new barrier function to solve a class of Semidefinite Optimization Problems (SOP) with bounded variables. That class is motivated by some (SOP) as the minimization of the sum of the first few eigenvalues of symmetric matrices and graph partitioning problems. We study the primal-dual central path defined by the new barrier and we show that this path is analytic, bounded and that all cluster points are optimal solutions of the primal-dual pair of problems. Then, using some...

On the central path for nonlinear semidefinite programming

L. M. Grana Drummond, Alfredo Noel Iusem, B. F. Svaiter (2010)

RAIRO - Operations Research

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In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective...