Airline seat inventory control is the allocation of seats in the same cabin to different fare classes such that the total revenue is maximized. Seat allocation can be modelled as dynamic stochastic programs, which are computationally intractable in network settings. Deterministic and probabilistic mathematical programming models are therefore used to approximate dynamic stochastic programs. The...

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...

This paper presents a smoothing heuristic for an NP-hard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty function. Starting points are drawn using different sampling techniques that use randomization and eigen...

Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an overview of the technique. We describe example algorithms, describe formal guarantees for the method, and describe practical issues in implementing the algorithm...

When does there exist an optimal generating Lagrangian multi-plier vector (that generates an optimal solution of an integer programming problem in a Lagrangian relaxation formulation), and in cases of nonexistence, can we produce the existence in some other equivalent representation space? Under what conditions does there exist an optimal primal-dual pair in integer programming? This paper cons...

Two heuristics for the Linear Ordering Problem are investigated in this paper. heuristics are embedded within a Lagrangian Relaxation framework and are initiated with a construction phase. In this process, some Lagrangian (dual) information is used as an input to guide the construction of initial Linear Orderings. Solutions thus obtained are then submitted to local improvement in an overall pro...

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with system lo...

In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the cone used is not...

In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the cone used is not...