Fclb.pdf">suppl; 1; 2013; 105; e245; in press
Abstract: In this paper we discuss the linear convergence of dual subgradient methods for the class of linearly constrained minimization problems. We introduce a new class of such problems, the so-called strictly convex linearly constrained problems. For this class we derive sufficient conditions for a single iteration and for the linear convergence. Moreover, a counter-example showing that the dual subgradient methods do not converge to the optimal solution in the sense of quadratic growth rate is given. Finally, a comparison of the proposed new framework with the standard dual-free framework is presented.
Translated abstract:
In this paper we discuss the linear convergence of dual subgradient methods for the class of linearly constrained minimization problems. We introduce a new class of such problems, the so-called strictly convex linearly constrained problems. For this class we derive sufficient conditions for a single iteration and for the linear convergence. Moreover, a counter-example showing that the dual subgradient methods do not converge to the optimal solution in the sense of quadratic growth rate is given. Finally, a comparison of the proposed new framework with the standard dual-free framework is presented.
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