Fast primal-dual algorithms via dynamics for linearly constrained convex optimization problems

By time discretization of a primal-dual dynamical system, we propose an inexact primal-dual algorithm, linked to the Nesterov's acceleration scheme, for the linear equality constrained convex optimization problem. We also consider an inexact linearized primal-dual algorithm for the composite problem with linear constrains. Under suitable conditions, we show that these algorithms enjoy fast convergence properties. Finally, we study the convergence properties of the primal-dual dynamical system to better understand the accelerated schemes of the proposed algorithms. We also report numerical experiments to demonstrate the effectiveness of the proposed algorithms

Robust Linear Neural Network for Constrained Quadratic Optimization

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper

A customized proximal point algorithm for convex minimization with linear constraints

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems. © 2013 Springer Science+Business Media New York.Link_to_subscribed_fulltex