The paper deals with the economic dispatch problem for a district heating system. The distribution network is modeled with a number of nodes and arcs, implying that time delays and restrictions in distribution capacity can be considered. A solution algorithm for the corresponding nonlinear optimization problem is proposed. The method is based on Lagrangian relaxation and exploits the relations ...

We analyse convex formulations for combined discrete-continuous MAP inference using the dual decomposition method. As a consquence we can provide a more intuitive derivation for the resulting convex relaxation than presented in the literature. Further, we show how to strengthen the relaxation by reparametrizing the potentials, hence convex relaxations for discrete-continuous inference does not ...

Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model – known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions – known as the M-Best MAP problem. In this paper, we propose an efficient message-pass...

In order to optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper we consider a streamlined version of this situation where a firm’s decision va...

The Lagrangian-doubly nonnegative (DNN) relaxation has recently been shown to provide effective lower bounds for a large class of nonconvex quadratic optimization problems (QOPs) using the bisection method combined with first-order methods by Kim, Kojima and Toh in 2016. While the bisection method has demonstrated the computational efficiency, determining the validity of a computed lower bound ...

Multi-depot Location-Routing Problem (MDLRP) is about finding the optimal number and locations of depots while allocating customers to depots and determining vehicle routes to visit all customers. In this study we propose a nested Lagrangian relaxation-based method for the discrete uncapacitated MDLRP. An outer Lagrangian relaxation embedded in subgradient optimization decomposes the parent pro...

We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and La-grangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

This paper deals with the multi-item capacitated lot-sizing problem with setup times and lost sales. Because lost sales, demands can be partially or totally lost. To find a good lower bound, we use a Lagrangian relaxation of the capacity constraints, when single-item uncapacitated lot-sizing problems with lost sales have to be solved. Each subproblem is solved using an adaptation of the O(T ) d...

We present a new method for the joint task of tagging and non-projective dependency parsing. We demonstrate its usefulness with an application to discontinuous phrase-structure parsing where decoding lexicalized spines and syntactic derivations is performed jointly. The main contributions of this paper are (1) a reduction from joint tagging and non-projective dependency parsing to the Generaliz...

When a manufacturer places repeated orders with a supplier to meet changing production requirements, he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes. We consider an inventory whose content fluctuates as a Brownian motion in the absence of control. At any moment, a controller can adjust the inventory lev...