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This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotra-type(More)
In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex(More)
We study different choices of search direction for primal-dual interior-point methods for semidefinite programming problems. One particular choice we consider comes from a specialization of a class of algorithms developed by Nesterov and Todd for certain convex programming problems. We discuss how the search directions for the Nesterov-Todd (NT) method can(More)
Interior point methods were widely used in the past in the form of barrier methods. In linear programming, the simplex method dominated, mainly due to inefficiencies of barrier methods. Interior point methods became quit popular again after 1984, when Karmarkar announced a fast polynomial-time interior method for nonlinear programming [Karmarkar, 1984]. In(More)