Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a nonlinear non-convex optimization problem. To obviate this shortcoming, we propose a new formulation as a multi-objective problem, with two objectives. The first one is the investment cost function or a suitable approximation of it; the second is the cost of energy that is required to transmit the gas. This energy cost is approximated by the total energy dissipated into the network. This bi-criterion problem turns out to be convex and easily solvable by convex optimization solvers. Our continuous optimization formulation can be used as an efficient continuous relaxation for problems with non-divisible restrictions such as a limited number of available commercial pipe dimensions.

This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier. Our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component. The paper also proposes an approximation scheme for the original objective. An active set strategy can be applied to the transfomed problem: it reduces the dimension of the dual space and accelerates computations. The new approach solves huge instances with high accuracy. The method is compared to alternative approaches proposed in the literature.

The energy sector is not only a major contributor to greenhouse gases, it is also vulnerable to climate change and will have to adapt to future climate conditions. The objective of this study is to analyze the impacts of changes in future temperatures on the heating and cooling services of buildings and the resulting energy and macro-economic effects at global and regional levels. For this purpose, the techno-economic TIAM-WORLD (TIMES Integrated Assessment Model) and the general equilibrium GEMINI-E3 (General Equilibrium Model of International-National Interactions between Economy, Energy and Environment) models are coupled with a climate model, PLASIM-ENTS (Planet-Simulator -Efficient Numerical Terrestrial Scheme). The key results are as follows. At the global level, the climate feedback induced by adaptation of the energy system to heating and cooling is found to be insignificant, partly because heating and cooling-induced changes compensate and partly because they represent a limited share of total final energy consumption. However, significant changes are observed at regional levels, more particularly in terms of additional power capacity required to satisfy additional cooling services, resulting in increases in electricity prices. In terms of macro-economic impacts, welfare gains and losses are associated more with changes in energy exports and imports than with changes in energy consumption for heating and cooling. The rebound effect appears to be non-negligible.To conclude, the coupling of models of different nature was successful and showed that the energy and economic impacts of climate change on heating and cooling remain small at the global level, but changes in energy needs will be visible at more local scale.

In this paper, we propose to solve the linear multicommodity flow problem using a partial Lagrangian relaxation. The relaxation is restricted to the set of arcs that are likely to be saturated at the optimum. This set is itself approximated by an active set strategy. The partial Lagrangian dual is solved with Proximal-ACCPM, a variant of the analytic center cutting plane method. The new approach makes it possible to solve huge problems when few arcs are saturated at the optimum, as it appears to be the case in many practical problems.Acknowledgments.