We present the moment cone (MC) relaxation and a hierarchy of sparse LagrangianSDP relaxations of polynomial optimization problems (POPs) using the unified framework established in Part I. The MC relaxation is derived for a POP of minimizing a polynomial subject to a nonconvex cone constraint and polynomial equality constraints. It is an extension of the completely positive programming relaxati...

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...

This paper describes an algorithm for exact decoding of phrase-based translation models, based on Lagrangian relaxation. The method recovers exact solutions, with certificates of optimality, on over 99% of test examples. The method is much more efficient than approaches based on linear programming (LP) or integer linear programming (ILP) solvers: these methods are not feasible for anything othe...

In object-based video, the encoding of the video data is decoupled into the encoding of shape, motion and texture information, which enables certain functionalities like content-based interactivity and scalability. However, the problem of how to jointly encode these separate signals to reach the best coding efficiency has never been solved thoroughly. In this paper, we present an operational ra...

This paper describes an algorithm for exact decoding of phrase-based translation models, based on Lagrangian relaxation. The method recovers exact solutions, with certificates of optimality, on over 99% of test examples. The method is much more efficient than approaches based on linear programming (LP) or integer linear programming (ILP) solvers: these methods are not feasible for anything othe...

Everyday, electricity generation companies submit a generation schedule to the grid operator for the coming day; computing an optimal schedule is called the unit-commitment problem. Generation companies can also occasionally submit changes to the schedule, that can be seen as intra-daily incomplete recourse actions. In this paper, we propose a two-stage formulation of unit-commitment, wherein b...

We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian rela...

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the unique path constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear ineq...