Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds. (4th March 2022) - Balashov, M. V.; Tremba, A. A.
Abstract : We analyse the convergence of the gradient projection algorithm, which is finalized with the Newton method, to a stationary point for the problem of nonconvex constrained optimization min x ∈ S f ( x ) with a proximally smooth set S = x ∈ R n : g ( x ) = 0 , g : R n → R m and a smooth function f . We propose new Error bound (EB) conditions for the gradient projection method which lead to the convergence domain of the Newton method. We prove that these EB conditions are typical for a wide class of optimization problems. It is possible to reach high convergence rate of the algorithm by switching to the Newton method.