This paper addresses the role of centrality in the implementation of interior point methods. Theoretical arguments are provided to justify the use of a symmetric neighbourhood. These are translated into computational practice leading to a new insight into the role of re-centering in the implementation of interior point methods. Arguments are provided to show that … Read more
In http://www.optimizationonline.org/DB_HTML/2005/05/1136.html 05/25/05, we have demonstrated that the family of all affine non-anticipative output-based control laws in a discrete time linear dynamical system affected by uncertain disturbances is equivalent, as far as state-control trajectories are concerned, to the family of all affine non-anticipative “purified-output-based” control laws. The advantage of the latter representation of affine controls … Read more
The main goals of this paper are to: i) relate two iteration-complexity bounds associated with the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming (LP), and; ii) study the geometrical structure of the central path in the context of LP. The first forementioned iteration-complexity bound is expressed in terms of an integral introduced by Sonnevend, Stoer and … Read more
In this paper, we propose a homogeneous model for solving monotone mixed complementarity problems over symmetric cones, by extending the results in \cite{YOSHISE04} for standard form of the problems. We show that the extended model inherits the following desirable features: (a) A path exists, is bounded and has a trivial starting point without any regularity … Read more
Computational results obtained when solving a subset of NETLIB problems by using a dense projected gradient implementation of the non-simplex active-set sagitta method presented in [12] are summarized. Two different addition rules for its initial phase are considered and, for each problem solved, two corresponding graphs are reported to illustrate the variations of the objective … Read more
The energy and properties of a many-electron atom or molecule may be directly computed from a variational optimization of a two-electron reduced density matrix (2-RDM) that is constrained to represent many-electron quantum systems. In this paper we implement a variational 2-RDM method with a representability constraint, known as the $T_2$ condition. The optimization of the … Read more
Semidefinite optimization, commonly referred to as semidefinite programming, has been a remarkably active area of research in optimization during the last decade. For combinatorial problems in particular, semidefinite programming has had a truly significant impact. This paper surveys some of the results obtained in the application of semidefinite programming to satisfiability and maximum-satisfiability problems. The … Read more
We define a variant of Anstreicher and Terlaky’s (1994) monotonic build-up (MBU) simplex algorithm for linear feasibility problems. Under a nondegeneracy assumption weaker than the normal one, the complexity of the algorithm can be given by $m\Delta$, where $\Delta$ is a constant determined by the input data of the problem and $m$ is the number … Read more
We study the problem of maximizing the second smallest eigenvalue of the Laplace matrix of a graph over all nonnegative edge weightings with bounded total weight. The optimal value is the \emph{absolute algebraic connectivity} introduced by Fiedler, who proved tight connections of this value to the connectivity of the graph. Using semidefinite programming techniques and … Read more
One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal-dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set … Read more