In this paper the authors study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratric form.

Problems dealing with the design and the operations of gas transmission networks arechallenging. The difficulty mainly arises from the simultaneous modeling of gastransmission laws and of the investment costs. The combination of the two yields a nonlinearnon-convex optimization problem. To...