We introduce a model-based excessive gap technique to analyze first-order primaldual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal feasibility gap of their iterates separately. Through a dual smoothing and prox-function selection strategy, our framework subsumes the augmented...

This paper shows, by means of a new type of operator called a splitting operator, that the Douglas-Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas-Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special...

We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Method of Multipliers (ADMM) to deal with complex regularization functions such as structured regularizations. Our method can naturally afford mini-batch update and it gives speed up of convergence. We show that, under mi...

The two state estimation mechanisms are investigated for the system with a randomly varying bias using only most recent finite measurements. One is the augmented filtering mechanism using the treatment of the bias as part of the system state. The other is the two-stage filtering mechanism using the linear combination of the outputs of a bias-free filter and a bias filter. It is shown that propo...

The alternating direction method of multipliers (ADMM) was proposed by Glowinski and Marrocco in 1975; and it has been widely used in a broad spectrum of areas, especially in some sparsitydriven application domains. In 1982, Fortin and Glowinski suggested to enlarge the range of the step size for updating the dual variable in ADMM from 1 to (0, 1+ √ 5 2 ); and this strategy immediately accelera...

A compositional performance certification method is presented for interconnected systems using subsystem dissipativity properties and the interconnection structure. A large-scale optimization problem is formulated to search for the most relevant dissipativity properties. The alternating direction method of multipliers (ADMM) is employed to decompose and solve this problem, and is demonstrated o...

Large convex quadratic programs, where constraints are of box type only, can be solved quite eeciently 1], 2], 12], 13], 16]. In this paper an exact quadratic augmented Lagrangian with bound constraints is constructed which allows one to use these methods for general constrained convex quadratic programming. This is in contrast to well known exact diierentiable penalty functions for this type o...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...

In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...