Optimization Seminar
Location
Mathematics/Psychology : 401
Date & Time
October 20, 2016, 10:30 am – 12:00 pm
Description
Title: Central Paths in Symmetric Cone Programming
Speaker: David Sossa, Universidad Técnica Federico Santa María, Valparaíso, Chile
Abstract:
In this talk we discuss the optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the existence and the convergence of primal, dual and primal-dual central paths. We are then able to establish concrete characterizations of the limit points of these central paths for specific subclasses. Indeed, for the class of barrier functions defined at the origin, we prove that the limit point of a primal central path minimizes the corresponding barrier function over the solution set of the studied symmetric cone program. In addition, we show that the limit points of the primal and dual central paths lie in the relative interior of the primal and dual solution sets for the case of the logarithm and modified logarithm barriers.
Speaker: David Sossa, Universidad Técnica Federico Santa María, Valparaíso, Chile
Abstract:
In this talk we discuss the optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the existence and the convergence of primal, dual and primal-dual central paths. We are then able to establish concrete characterizations of the limit points of these central paths for specific subclasses. Indeed, for the class of barrier functions defined at the origin, we prove that the limit point of a primal central path minimizes the corresponding barrier function over the solution set of the studied symmetric cone program. In addition, we show that the limit points of the primal and dual central paths lie in the relative interior of the primal and dual solution sets for the case of the logarithm and modified logarithm barriers.
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