The SU(2) collective coordinates quantization of the Born-Infeld Skyrmions Lagrangean is performed. The obtainment of the classical Hamiltonian from this special Lagrangean is made by using an approximate way: it is derived from the expansion of this non-polynomial Lagrangean up to second-order variable in the collective coordinates, using for this some causality arguments. Because this system ...

In this work, we address the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We first propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity...

We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (2010) and uses Benders decomposition to form a master problem and a subproblem. The new...

In optimal short-term resource scheduling decomposition and coordination methods by Lagrangean relaxation are known as convenient to handle resource-specific constraints and for their ability to provide duality gap estimates. They will be used, in context of subgradient optimization, to deal with this problem. One cause of erratic behavior often encountered in subgradient optimization is associ...

In this paper we consider an extended version of the classical capacitated single allocation hub location problem in which the size of the hubs must be chosen from a finite and discrete set of allowable capacities. We develop a Lagrangian relaxation approach that exploits the problem structure and decomposes the problem into a set of smaller subproblems that can be solved efficiently. Upper bou...

We consider the Linking Set Problem which occurs as a subproblem in a decomposition procedure to solve large scale p-median problems such as the Optimal Diversity Management Problem. We show that a greedy algorithm solves the Linking Set Problem when the costs have a special structure. This special structure usually occurs when the Linking Set Problem arises from the decomposition of location p...

We consider in this paper a new lagrangean relaxation with clusters for the Manufacturer’s Pallet Loading Problem (MPLP). The relaxation is based on the MPLP formulated as a Maximum Independent Set Problem (MISP) and represented in a conflict graph that can be partitioned in clusters. The edges inter clusters are relaxed in a lagrangean fashion. Computational tests attain the optimality for som...

In this work we apply a decomposition technique to address the simultaneous scheduling and optimal control problem of multi-grade polymerization reactors. The simultaneous scheduling and control (SSC) problem is reformulated using Lagrangean Decomposition as presented by Guignard and Kim1. The resulting model is decomposed into scheduling and control subproblems, and solved using a heuristic ap...