Error bound conditions and convergence of optimization methods on smooth and proximally smooth manifolds. (4th March 2022)

• Record Type: Journal Article
• Authors: Balashov, M. V.; Tremba, A. A.
• Is Part Of: Optimization. Volume 71:Number 3(2022)
• Page Start: 711
• Page End: 735
• Publication Date: 2022-03-04
• Subjects: Error bound condition -- gradient projection algorithm -- Newton's method -- nonconvex optimization -- proximal smoothness; Primary: 90C26 -- 65K05 -- Secondary: 46N10 -- 65K10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1812066
• Languages: English
• ISSNs: 0233-1934

Abstract

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.