When applied to large-scale separable optimization problems, the recently developed surrogate subgradient method for Lagrangian relaxation (Zhao et al.: J. Optim. Theory Appl. 100, 699–712, 1999) does not need to solve optimally all the subproblems to update the multipliers, as the traditional subgradient method requires. Based on it, the penalty surrogate subgradient algorithm was further deve...

This paper investigates convex belief propagation algorithms for Markov random fields (MRFs) with continuous variables. Our first contribution is a theorem generalizing properties of the discrete case to the continuous case. Our second contribution is an algorithm for computing the value of the Lagrangian relaxation of the MRF in the continuous case based on associating the continuous variables...

In this paper we develop and test a distributed algorithm providing Energy Consumption Schedules (ECS) in smart grids for a residential district. The goal is to achieve a given aggregate load profile. The NP-hard constrained optimization problem reduces to a distributed unconstrained formulation by means of Lagrangian Relaxation technique, and a meta-heuristic algorithm based on a Quantum inspi...

Due to its relatively high total energy eeciency, the application of cogeneration is attracting increased attention. Today cogeneration is an essential element in the energy supply system in many countries, and when environmental and economic aspects are considered too, it seems to be a relevant option in expansion planning in many situations. The present paper presents a quite general and yet ...

We describe computational procedures to solve a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets’ progressive hedging algorithm. Experiments demonstrate ...

The satellite scheduling community has provided several algorithms for allocating interaction windows between ground stations and satellites, from simple greedy approaches to more complex hybrid-genetic or Lagrangian-relaxation techniques. Single-location ground station problems, where requests have fixed time intervals and no priorities, are known to be solvable in polynomial time. To the best...

In this paper, we propose Lagrangian relaxation technique for solving scheduling problems by decomposition of timed Petri nets. The scheduling problem is represented by the transition firing sequence problem to minimize a given objective function. The timed Petri net is decomposed into several subnets so that the subproblem for each subnet can be easily solved by a shortest path algorithm. The ...

The paper shows that the use of a memetic algorithm (MA), a genetic algorithm (GA) combined with local search, synergistically combined with Lagrangian relaxation is effective and efficient for solving large unit commitment problems in electric power systems. It is shown that standard implementations of GA or MA are not competitive with the traditional methods of dynamic programming (DP) and La...

We study the problem of finding a minimum weight connected subgraph spanning at least k vertices on planar, node-weighted graphs. We give a (4 + ε)-approximation algorithm for this problem. In the process, we use the recent LMP primal-dual 3-approximation for the node-weighted prize-collecting Steiner tree problem [4] and the Lagrangian relaxation [6]. In particular, we improve the procedure of...

We propose a Uzawa block relaxation domain decomposition method for a two-body contact problem with Tresca friction. We introduce auxiliary interface unknowns to transform the variational problem into a saddle-point problem. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional we obtain a domain decomposition algorithm in which we have to solve two un...