Approaching Nonsmooth Nonconvex Optimization Problems Through First Order Dynamical Systems with Hidden Acceleration and Hessian Driven Damping Terms

作者：Bot Radu Ioan^*; Csetnek Ernoe Robert

来源：Set-Valued and Variational Analysis, 2018, 26(2): 227-245.

DOI：10.1007/s11228-017-0411-1

• Dynamical systems
• Lyapunov analysis
• Nonsmooth optimization
• Limiting subdifferential
• Kurdyka-Lojasiewicz property

In this paper we carry out an asymptotic analysis of the proximal-gradient dynamical system where f is a proper, convex and lower semicontinuous function, I broken vertical bar a possibly nonconvex smooth function and gamma,a and b are positive real numbers. We show that the generated trajectories approach the set of critical points of f + I broken vertical bar, here understood as zeros of its limiting subdifferential, under the premise that a regularization of this sum function satisfies the Kurdyka-Aojasiewicz property. We also establish convergence rates for the trajectories, formulated in terms of the Aojasiewicz exponent of the considered regularization function.

• 出版日期2018-6