Joint chance-constrained optimization problems under discrete distributions arise frequently in financial management and business operations. These can be reformulated as mixed-integer programs. The size of integer programs is usually very large even though the original problem medium size. This paper studies an augmented Lagrangian decomposition method for finding high-quality feasible solutio...

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...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with ramp rate, emission and transmission constraints. The proposed ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian function. In ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty ...

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...