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 present a new derivative-free trust-region (DFTR) algorithm to solve general nonlinear constrained problems with the use of an augmented Lagrangian method. No derivatives are used, neither for the objective function nor for the constraints. An augmented Lagrangian method, known as an effective tool to solve equality and inequality constrained optimization problems with derivatives, is exploi...

In this letter, we formulate the model reduction problem of a stable and positive network system as constrained Riemannian optimization with $H^{2}$ -error objective function original reduced systems. We improve performance clustering...

Abstract This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for solution optimization problems with geometric constraints. Specifically, we study situations where parts constraints are nonconvex possibly complicated, but allow a fast computation projections onto this set. Typical problem classes which satisfy requirement disjunctive (like comp...

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with system lo...