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A simple column generation scheme that employs an interior point method to solve underlying restricted master problems is presented. In contrast with the classical column generation approach where restricted master problems are solved exactly, the method presented in this paper consists in solving it to a predetermined optimality tolerance (loose at the(More)
The paper deals with nonlinear multicommodity ow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to deene a sequence of primal linear programming problems. Each subproblem consists of nding a minimum(More)
Issues of implementation of an object-oriented library for parallel interior-point methods are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modelled. The efficiency of(More)
A new concept is proposed for linking algebraic modeling language and the structure exploiting solver. SPI (Structure Passing Interface) is a program that enables retrieving structure from the anonymous mathematical program built by the algebraic modeling language. SPI passes the special structure of the problem to a SES (Structure Exploiting Solver). An(More)
We addres some of the issues that arise when an interior point method is used to handle the master problem in a decomposition approach. The main points concern the eecient exploitation of the special structure of the master problem to reduce the cost of a single interior point iteration. The particular structure is the presence of GUB constraints and the(More)
A telecommunication network is survivable if, following an arc failure, the interrupted traac can be redirected through the network via existing excess capacity. The standard survivability problem consists in nding the least cost investment in spare capacity to allow rerouting of a given base traac. In this paper we consider the more involved problem of(More)
We use a decomposition approach to solve three types of realistic problems: block-angular linear programs arising in energy planning, Markov decision problems arising in production planning and multicommodity network problems arising in capacity planning for survivable telecommunication networks. Decomposition is an algorithmic device that breaks down(More)
Extracting complex block structures from an anonymous mathematical program is a difficult task. It is however a mandatory step to exploit them with adequate algorithmic techniques. Moreover, most economic models are usually built with an Algebraic Modeling Language (AML) which loose any structure. The recently developed concept SET (Structure Exploiting(More)
Most of the applied models written with an algebraic modeling language involve simultaneously several dimensions such as materials, location, time or uncertainty. The information about dimensions available in the algebraic formulation is usually suucient to retrieve diierent block structures from mathematical programs. These structured problems can then be(More)