We introduce a new barrier function to solve a class ofSemidefinite Optimization Problems (SOP) with bounded variables.That class is motivated by some (SOP) as the minimization of thesum of the first few eigenvalues of symmetric matrices and graphpartitioning problems. We study the primal-dual central pathdefined by the new barrier and we show that this path is analytic,bounded and that all cluster points are optimal solutions of theprimal-dual pair of problems. Then, using some ideas fromsemi-analytic geometry we prove its full convergence. Finally, weintroduce a new proximal point algorithm for that class ofproblems and prove its convergence.
