In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within the framework of inexact-ADMM. It requires a communication graph for the information exchange between the players as well as a few mild assumptions on cost f...

The Augmented Lagrangean Relaxation (ALR) method is one of the most powerful techniques to solve the Short-Term Hydrothermal Coordination (STHC) problem. A crucial step when using the ALR method is the updating of the multipliers. In this paper we present a new multiplier updating procedure: the Gradient with Radar Step (GRS) method. The method has been successfully tested by solving medium-sca...

Multi-label learning methods assign multiple labels to one object. In practice, in addition to differentiating relevant labels from irrelevant ones, it is often desired to rank the relevant labels for an object, whereas the rankings of irrelevant labels are not important. Such a requirement, however, cannot be met because most existing methods were designed to optimize existing criteria, yet th...

We investigate the hypothesis that word representations ought to incorporate both distributional and relational semantics. To this end, we employ the Alternating Direction Method of Multipliers (ADMM), which flexibly optimizes a distributional objective on raw text and a relational objective on WordNet. Preliminary results on knowledge base completion, analogy tests, and parsing show that word ...

Adaptive augmented Lagrangian methods: algorithms and practical numerical experience Frank E. Curtis, Nicholas I.M. Gould, Hao Jiang & Daniel P. Robinson a Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA b STFC-Rutherford Appleton Laboratory, Numerical Analysis Group, R18, Chilton, OX11 0QX, UK c Department of Applied Mathematics and Statistics, Johns Hop...

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...