Monday, 16:15 - 16:40 h, Room: H 2038

 

Renato Monteiro
An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods

Coauthor: Benar F. Svaiter

 

Abstract:
We present an accelerated variant of the hybrid proximal
extragradient (HPE) method for convex optimization,
referred to as the A-HPE method.
Iteration-complexity results are established for
the A-HPE method, as well as a special version of it,
where a large stepsize condition is imposed.
Two specific implementations of the A-HPE method are described in the context
of a structured convex optimization problem whose objective function consists
of the sum of a smooth convex function and an extended real-valued non-smooth
convex function. In the first implementation, a generalization of a variant of
Nesterov's method is obtained for the case where the smooth component
of the objective function has Lipschitz continuous gradient.
In the second one, an accelerated Newton proximal extragradient
(A-NPE) method is obtained for the case where the smooth component of
the objective function has Lipschitz continuous Hessian. It is shown that
the A-NPE method has a O(1/k7/2) convergence rate,
which improves upon the O(1/k3)
convergence rate bound for another accelerated Newton-type
method presented by Nesterov.

 

Talk 3 of the invited session Mon.3.H 2038
"Matrix optimization" [...]
Cluster 4
"Conic programming" [...]

 

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