We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modelling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particu...

We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian framework. We analyze its convergence and provide an application to two network models, as well as to a two-stage stochastic optimization problem. The proposed method compares favorably to two augmented Lagrangian decomposition methods kno...

Dual decomposition has been recently proposed as a way of combining complementary models, with a boost in predictive power. However, in cases where lightweight decompositions are not readily available (e.g., due to the presence of rich features or logical constraints), the original subgradient algorithm is inefficient. We sidestep that difficulty by adopting an augmented Lagrangian method that ...

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to bot...

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...

We consider solving nonlinear programming problems using an augmented Lagrangian method that makes use of derivative-free generating set search to solve the subproblems. Our approach is based on the augmented Lagrangian framework of Andreani, Birgin, Mart́ınez, and Schuverdt which allows one to partition the set of constraints so that one subset can be left explicit, and thus treated directly wh...

This paper proposes an augmented Lagrangian Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN is the continuous Hopfield neural network based on augmented Lagrangian relaxation as its energy function. In the proposed ALHN, its energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagrangian re...

Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and...