In this paper we consider a new analytic center cutting plane method in a projective space. We prove the efficiency for the general scheme and show that these results can be used in the analysis of a feasability problem, the variational inequality problem and the problem if constrained...

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the efficiency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained...

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 non- linear non-convex optimization problem. To...

This paper deals with an application of a variant of Karmarkar's projective algorithm for linear programming to the solution of a generic nondifferentiable minimization problem. This problem is closely related to the Dantzig-Wolfe decomposition technique used in large-scale convex programming....

We analyze the process of a two cut generation scheme in the analytic center cutting plane method. We propose an optimal restoration when the two cuts are central.

A new concept is proposed for linking algebraic modeling languages and the structure exploiting solver.