A second-order dynamical approach with variable damping to nonconvex smooth minimization. Issue 3 (17th February 2020)

• Record Type: Journal Article
• Authors: Boţ, Radu Ioan; Csetnek, Ernö Robert; László, Szilárd Csaba
• Is Part Of: Applicable analysis. Volume 99:Issue 3(2020)
• Page Start: 361
• Page End: 378
• Publication Date: 2020-02-17
• Subjects: Boris Mordukhovich; Second-order dynamical system -- nonconvex optimization -- Kurdyka–Łojasiewicz inequality -- convergence rate; 90C26 -- 90C30 -- 65K10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1495330
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We investigate a second-order dynamical system with variable damping in connection with the minimization of a nonconvex differentiable function. The dynamical system is formulated in the spirit of the differential equation which models Nesterov's accelerated convex gradient method. We show that the generated trajectory converges to a critical point, if a regularization of the objective function satisfies the Kurdyka- Lojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the Lojasiewicz exponent.