Primal-dual interior-point methods with asymmetric barriers

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Guest Lecturer:
Dr. Yuri Nesterov
Catholic University at Louvain-la-Neuve, Belgium

Presentation Title: Primal-dual interior-point methods with asymmetric barriers

Very often, in the standard optimization problem with general cone constraints, the natural self-concordant barriers for primal and dual cones are not self-conjugate. Geometric programming and the power cones provide us with the most important examples. This primal-dual asymmetry destroys the good properties of the primal-dual barrier function. As a result, the standard machinery of the long-step infeasible-start primal-dual methods does not work.
In this talk, we show that even in the asymmetric case, the interior-point methods remain a powerful computational tool. We discuss several potential-reduction and path following primal-dual schemes. We show that some of them can be implemented in a matrix-free way. This opens a possibility for a direct competition of these polynomial-time methods with recently revived fast gradient schemes, which are applicable to very large optimization problems.


  • Workflow Status: Published
  • Created By: Barbara Christopher
  • Created: 10/12/2009
  • Modified By: Fletcher Moore
  • Modified: 10/07/2016

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