Accelerated Primal-Dual Projection Neurodynamic Approach With Time Scaling for Linear and Set Constrained Convex Optimization Problems

You Zhao, Xing He, Mingliang Zhou

Abstract:

The Nesterov accelerated dynamical approach serves
as an essential tool for addressing convex optimization problems
with accelerated convergence rates. Most previous studies in this
field have primarily concentrated on unconstrained smooth convex optimization problems. In this paper, on the basis of primaldual dynamical approach, Nesterov accelerated dynamical
approach, projection operator and directional gradient, we
present two accelerated primal-dual projection neurodynamic
approaches with time scaling to address convex optimization
problems with smooth and nonsmooth objective functions subject
to linear and set constraints, which consist of a second-order ODE
(ordinary differential equation) or differential conclusion system
for the primal variables and a first-order ODE for the dual variables. By satisfying specific conditions for time scaling, we
demonstrate that the proposed approaches have a faster convergence rate. This only requires assuming convexity of the objective
function. We validate the effectiveness of our proposed two accelerated primal-dual projection neurodynamic approaches through
numerical experiments.