in this paper, a facility location problem of distribution systems, as one of the important and strategic issues in supply chain management, has been studied in a three-level supply chain under a stochastic condition. for this purpose, a two-stage mathematic model has been proposed for the location-allocation problem of distribution systems with regard to backup facilities for disrupting wareho...

We propose an efficient computational method for linearly constrained quadratic optimization problems (QOPs) with complementarity constraints based on their Lagrangian and doubly nonnegative (DNN) relaxation and first-order algorithms. The simplified Lagrangian-CPP relaxation of such QOPs proposed by Arima, Kim, and Kojima in 2012 takes one of the simplest forms, an unconstrained conic linear o...

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...

An improved Lagrangian relaxation (LR) solution to the thermal unit commitment problem (UCP) is proposed in this paper. The algorithm is characterized by: (1) a new Matlab function to determine the optimal path of the dual problem, (2) new initialization procedure of Lagrangian multipliers, based on both unit and time interval classification, (3) a flexible adjustment of Lagrangian multipliers,...

It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian relaxation. It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal s...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed. The immediate event that triggered my interest in this topic occurred early in 1971 in connection with...