In this article, a free-time impulsive control problem with state constraints and equality and inequality constraints on the trajectory endpoints is considered. A weakened maximum principle is obtained for problems with data measurable in the time variable, being the time transversality conditions deduced with the help of some extra convexity assumption on the state constraints. In the case of ...

An iterative method is presented which gives an optimum approximation to the joint probability distribution of a set of binary variables given the joiat probability distributions of any subsets of the variables (any set of component distributions). The most significant feature of this approximation procedure is that there is no limitation to the number or type of component distributions that ca...

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme using a smoothed fast gradient method that is equipped with explicit bounds on the approximation error. We further demonstrate how the prese...

One method for building classification trees is to choose split variables by maximising expected entropy. This can be extended through the application of imprecise probability by replacing instances of expected entropy with the maximum possible expected entropy over credal sets of probability distributions. Such methods may not take full advantage of the opportunities offered by imprecise proba...

in this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. next, some numerical solutions are considered for the cases of unavailable closed form of solutions. finally, these methods are illustrated via some numerical examples.

This paper presents a new weighted entropy-based measure for assessing reliability of water distribution networks. The proposed methodology considers both of mechanical uncertainties (probability of pipe failure) and uncertainties due to hydraulic parameters (flow in pipe) simultaneously. In this methodology a penalty function is defined for different links of the network based on their probabi...