We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is prese...

The alternating direction of multipliers (ADMM) is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problems arising from “big data” and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational environments. This chapter aims to provide an ac...

We propose an efficient numerical algorithm for computing deformations of “very” soft tissues (such as the brain, liver, kidney etc.), with applications to real time surgical simulation. The algorithm is based on the finite element method using the Total Lagrangian formulation, where stresses and strains are measured with respect to the original configuration. This choice allows for pre-computi...

The alternating direction of multipliers (ADMM) is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problems arising from “big data” and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational environments. While it is easiest to describe th...

In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newto...

In this work we address the Quadratic Minimum Spanning Tree Problem (QMSTP) known to be NP-hard. Given a complete graph, the QMSTP consists of determining a minimum spanning tree (MST) considering interaction costs between pairs of edges to be modelled. A Lagrangian relaxation procedure is devised and an efficient local search algorithm with tabu thresholding is developed. Computational experim...