Generalized nesterov’s algorithm for constrained minimization problems on closed convex sets

Abstract

In this paper, we propose a generalized Nesterov algorithm for the constrained optimization problems on a closed convex set. We prove the convergence as well as the convergence rate of the proposed algorithm. First, we present a new algorithm based on the generalization of Nesterov’s algorithm. Then, we prove the convergence as well as the convergence rate of the new algorithm. With a specific choice of parameters, the new algorithm becomes Nesterov’s algorithm. Therefore, the convergence as well as the convergence rate of Nesterov’s algorithm are also followed. We illustrate the effectiveness of the new algorithm as well as compare it with Nesterov’s algorithm and the gradient descent algorithm through a specific example.

Keywords

• constrained minimization problem
• closed convex set
• nesterov’s algorithm
• convergence
• convergence rate