On the central paths and Cauchy trajectories in semidefinite programming

Title:

On the central paths and Cauchy trajectories in semidefinite programming

Creator:

López, Julio and Ramírez C., Héctor

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:880e1c2b-a6d3-4923-b21b-91a689e2e75f
uuid:880e1c2b-a6d3-4923-b21b-91a689e2e75f

Subject:

semidefinite programming, central paths, penalty/barrier functions, Riemannian geometry, and Cauchy trajectories

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this work, we study the properties of central paths, defined with res\-pect 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 primal-dual) central path toward a (primal, dual, primal-dual, 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[524]-535

Source:

Kybernetika | 2010 Volume:46 | Number:3

Harvested from:

CDK

Metadata only:

false