چکیده:
In this paper, we present a new primal-dual interior-point algorithm based on a new
large neighbourhood (t ,B ) N for semidefinite optimization. This large
neighbourhood is based on the infinity norm. It is larger than the N( , ) large
neighborhood of the central path, which is popular wide neighborhood. We
demonstraite the convergence of the proposed algorithm and show that the
algorithm has ( log ) 121loge p O n iteration complexity bound for the Nesterov-Todd
direction.
خلاصه ماشینی:
ir Received: January 2020 Accepted: February 2020 Abstract In this paper, we present a new primal-dual interior-point algorithm based on a new large neighbourhood for semidefinite optimization.
Keywords: Semidefinite optimization, wide neighborhood, interior-point method, iteration complexity bound.
Let us choose proposed by Nesterov and Todd [4] where (به تصویر صفحه مراجعه شود) Clearly, the NT scaling matrix satisfies .
In this paper, we introduce a new neighborhood for the central path similar to [2 as follows: (به تصویر صفحه مراجعه شود) where are given constants.
We compute the search directions by solving the following system:(به تصویر صفحه مراجعه شود) Let the new iterate be given by where .
Then Algorithm 1 will terminate in iterations with a solution for which (به تصویر صفحه مراجعه شود) 6- Conclusions In this paper, we proposed a new primal-dual interior-point algorithm for SDO problems acting in a new large neighborhood.