We present the technical background material for a version of the Pontryagin Maximum Principle with state space constraints and very weak technical hypotheses, based on a primal approach that uses generalized differentials and packets of needle variations. In particular, we give a detailed account of two theories of generalized differentials, the " generalized differential quotients " (GDQs) an...

In [14] M.G.Platone Garroni has extended the classical generalized maximum principle (see, for instance, [15]), when the coefficients of the operator are discontinuous, to subsolutions of elliptic linear second order equations with mixed type boundary unilateral conditions, that is, on a portion of the boundary ∂Ω of Ω, the values of the solution are assigned, while on the other part a unilater...

The Maximum Entropy Modeling Toolkit supports parameter estimation and prediction for statistical language models in the maximum entropy framework. The maximum entropy framework provides a constructive method for obtaining the unique conditional distribution p*(y|x) that satisfies a set of linear constraints and maximizes the conditional entropy H(p|f) with respect to the empirical distribution...

We give a simple proof of the Maximum Principle for smooth hybrid control systems by reducing the hybrid problem to an optimal control problem of Pontryagin type and then by using the classical Pontryagin Maximum Principle.

We start this talk posing the question, is there any physical principle that can serve as a selection principle in biology too? One of the first undertakings in this direction, conducted by Prigogine and Wiame [1] noticed correctly that biological processes are irreversible and as such should be described within irreversible thermodynamics. Since irreversible processes are characterized by entr...