Accelerated Projection Neurodynamic Approach for Convex Optimization with Affine Equality and Inequality Constraints

This paper presents an accelerated projection neurodynamic approach to deal with convex optimization issues that involve affine equality, inequality, and set constraints. The approach comprises two first-order projection ordinary differential equations (ODEs) for primal variables, two first-order ODEs for dual variables of the equation constraint, and two first-order projection ODEs for dual variables of the inequality constraint. A new projection strategy is introduced for the optimization variables and the dual variables of inequality constraints. This strategy not only can ensure the optimality of the neurodynamic method but also can be well integrated with the primal-dual dynamic method and the Nesterov accelerated dynamic method. By meeting specific parameter conditions, it is shown that the presented approach possesses a fast convergence rate comparable to that of the Nesterov accelerated gradient method. The effectiveness of the proposed projection neurodynamic approach is validated through numerical experiments.