OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

16.00h: "Second-order methods with provable global complexity"
Yurii Nesterov (UCL CORE)

In this talk, we discuss a recent progress in the general second-order
minimization schemes related to the cubic regularization of the Newton's
method. For convex case, we present an accelerated multistep version of the method.
We consider the extensions of the new schemes onto constrained problems.
Preliminary computational results are also discussed.

Slides

17.00h: "An augmented primal-dual method for linear conic minimization"
 Florian Jarre (University of Duesseldorf),  Franz Rendl  (University of Klagenfurt)

 We present a new iterative method for solving linear minimization problems
 over convex cones. The problem is reformulated as an unconstrained problem of
 minimizing a differentiable convex function. The method does not use any
 homotopy parameter but solves the primal-dual problem in one step using a
 nonlinear conjugate gradient type approach. In the case of a semidefinite program
 we  propose a regularizing function that makes the generalized Hessian positive
 definite when there is a unique and strictly complementary optimal solution.
 Numerical examples for some classes of difficult semidefinite programs illustrate
 the potential of the new approach.

Slides