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**Harvard**

Gustavsson, E., Patriksson, M. och Strömberg, A. (2012) *Primal convergence from dual subgradient methods for convex optimization*.

** BibTeX **

@unpublished{

Gustavsson2012,

author={Gustavsson, Emil and Patriksson, Michael and Strömberg, Ann-Brith},

title={Primal convergence from dual subgradient methods for convex optimization},

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 that define the ergodic sequence of primal solutions. In contrast to previously proposed rules, 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 ones previously proposed.},

year={2012},

keywords={Convex programming, Lagrangian duality, subgradient optimization, ergodic convergence, nonlinear multicommodity ﬂow problem},

note={22},

}

** RefWorks **

RT Unpublished Material

SR Print

ID 165918

A1 Gustavsson, Emil

A1 Patriksson, Michael

A1 Strömberg, Ann-Brith

T1 Primal convergence from dual subgradient methods for convex optimization

YR 2012

AB 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 that define the ergodic sequence of primal solutions. In contrast to previously proposed rules, 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 ones previously proposed.

LA eng

OL 30