Abstract
The auxiliary problem principle has been widely applied in power systems to solve the multi-area economic dispatch problem. Although the effectiveness and correctness of the auxiliary problem principle method have been demonstrated in relevant literatures, the aspect connected with accurate estimate of its convergence rate has not yet been established. In this paper, we prove the O ( 1 / n ) convergence rate of the auxiliary problem principle method.
Highlights
The auxiliary problem principle (APP) [1], originally proposed by G
For solving (1), the corresponding APP iterative scheme can be expressed as follows
In 2004, Nemirovski gave a proof to show that prox-type method has the O(1/n) convergence rate for variational inequalities with Lipschitz continuous monotone operators, where n denotes the iteration number [10]
Summary
The auxiliary problem principle (APP) [1], originally proposed by G. The APP iterative scheme is known to be an efficient approach for the convex problem with separable operators [9], the theoretical analysis of its convergence rate has not been established and applied in the literature. In 2004, Nemirovski gave a proof to show that prox-type method has the O(1/n) convergence rate for variational inequalities with Lipschitz continuous monotone operators, where n denotes the iteration number [10]. For the same problem, the O(1/n) convergence rate of the projection and contraction method was proved in [11] Inspired by these literatures, taking advantage of the variational inequality approach, the accurate estimate of alternating direction method’s convergence rate has made considerable headway in recent years.
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