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

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 primal-dual 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.