  


On the Central Paths and Cauchy Trajectories in Semidefinite Programming
Julio Lopez(jclopezdim.uchile.cl) Abstract: In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular case of convex programming with conic constraints. The studied class of functions consists of spectrally defined functions induced by penalty or barrier maps defined over the real nonnegative numbers. We prove the convergence of the (primal, dual and primaldual) central path toward a (primal, dual, primaldual, respectively) solution of our problem. Finally, we prove the global existence of Cauchy trajectories in our context and we recall its relation with primal central path when linear semidefinite programs are considered. Some illustrative examples are shown at the end of this paper. Keywords: Semidefinite programming, central paths, penalty/barrier functions, Riemannian geometry, Cauchy trajectories. Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: DIMCMM N: CMMB09/08227, Universidad de Chile, Aug/2009. Download: [Postscript][PDF] Entry Submitted: 09/01/2009 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  