Tuesday, 14:15 - 14:40 h, Room: H 1012

 

Emil Gustavsson
Primal convergence from dual subgradient methods for convex optimization

Coauthors: Michael Patriksson, Ann-Brith Strömberg

 

Abstract:
When solving a convex optimization problem through a Lagrangian dual reformulation subgradient optimization methods are favourably utilized, since they often find near-optimal dual solutions quickly. However, an optimal primal solution is generally not obtained directly through such a subgradient approach. We construct a sequence of convex combinations of primal subproblem solutions, a so called ergodic sequence, which is shown to converge to an optimal primal solution when the convexity weights are appropriately chosen. We generalize previous convergence results from linear to convex optimization and present a new set of rules for constructing the convexity weights defining the ergodic sequence of primal solutions. In contrast to rules previously proposed, they exploit more information from later subproblem solutions than from earlier ones. We evaluate the proposed rules on a set of nonlinear multicommodity flow problems and demonstrate that they clearly outperform the previously proposed ones.

 

Talk 3 of the invited session Tue.2.H 1012
"Nonsmooth optimization methods" [...]
Cluster 17
"Nonsmooth optimization" [...]

 

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