Robert Sarkissian

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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)
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)
It is proposed that traac in a telecommunications network be secured in the event of a node or link failure by the rerouting of traac over a reserve network. The problem consists of two related parts: the dimensioning of a reserve network, and the reallocation , or rerouting of traac. We formulate the problem as a linear programming problem of huge size(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 sucient to retrieve dierent block structures from mathematical programs. These structured problems can then be(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)
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