A novel relaxation labeling (RL) method is presented based on Augmented Lagrangian multipliers and the graded Hoppeld neural network (ALH). In this method, an RL problem is converted into a constrained optimization problem and solved by using the augmented Lagrangian and Hoppeld techniques. The ALH method yields results comparable to the best of the existing RL algorithms in terms of the optimi...

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago, ADMM so far can be applied only to unconstrained problems and problems with...

A globally and quadratically convergent primal–dual augmented Lagrangian algorithm for equality constrained optimization Paul Armand & Riadh Omheni To cite this article: Paul Armand & Riadh Omheni (2015): A globally and quadratically convergent primal–dual augmented Lagrangian algorithm for equality constrained optimization, Optimization Methods and Software, DOI: 10.1080/10556788.2015.1025401 ...

Shape-constrained convex regression problem deals with fitting a function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides unified framework for computing least squares estimator of multivariate shape-constrained in $${\mathbb {R}}^d$$ . We prove that is computable via solving an essentially...