Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal integer solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instan...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...

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 ...

‎By p-power (or partial p-power) transformation‎, ‎the Lagrangian function in nonconvex optimization problem becomes locally convex‎. ‎In this paper‎, ‎we present a neural network based on an NCP function for solving the nonconvex optimization problem‎. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimizatio...

A cross-layer network optimization problem is considered. It involves network and transport layers, treating both routing and flows as decision variables. Due to the nonconvexity of the capacity constraints, when using Lagrangian relaxation method a duality gap causes numerical instability. It is shown that the rescue preserving separability of the problem may be the application of the augmente...

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...

Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and bound bound methods for solving certain classes of nonconvex optimization problems by reducing the duality gap. We discuss this method for the class of partly linear and partly convex optimization problems and, incidentally, point out incorrect results in the recent literature on this sub...

To improve thequalityofdecisionmaking in theprocessoperations, it is essential to implement integrated planning and scheduling optimization. Major challenge for the integration lies in that the corresponding optimization problem is generally hard to solve because of the intractable model size. In this paper, ccepted 18 November 2009 vailable online 24 November 2009 eywords: lanning and scheduli...