In this section, we introduce one of the most important ideas in economic modelling, in the theory of optimization and, indeed in much of modern analysis and computatyional mathematics: that of a convex set. Almost every situation we will meet will depend on this geometric idea. As an independent idea, the notion of convexity appeared at the end of the 19 century, particularly in the works of M...

This paper deals with the simulation of hybrid systems. These systems mix two different aspects: continuous and discrete. Their simulation presents many problems mainly the synchronisation between the two models. Stateflow, used to describe the discrete model, is co-ordinated with Matlab, used to describe the continuous model. The gas storage example is used to illustrate the co-ordination of t...

‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...