‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

We consider discrete-time Markov control processes with Borel state and control spaces, unbounded costs per stage and not necessarily compact control constraint sets. The basic control problem we are concerned with is to minimize the infinite-horizon, expected total discounted cost. Under easily verifiable assumptions, we provide characterizations of the optimal cost function and optimal polici...

We provide a complete solution to a general, continuous-time dynamic allocation (multi-armed bandit) problem with arms that are not necessarily independent or Markovian, using notions and results from time-changes, optimal stopping, and multi-parameter martingale theory. The independence assumption is replaced by the condition (F.4) of Cairoli & Walsh. We also introduce a synchronization identi...

We generalise classical multi-armed and restless bandits to allow for the distribution of a (fixed amount of a) divisible resource among the constituent bandits at each decision point. Bandit activation consumes amounts of the available resource which may vary by bandit and state. Any collection of bandits may be activated at any decision epoch provided they do not consume more resource than is...

We consider the (sub)optimal H∞-control problem for discrete time descriptor systems. Necessary and su cient optimality conditions are derived in terms of de ating subspaces of palindromic matrix pencils. This approach allows the use of structure preserving matrix techniques which lead to a more robust method compared with currently used algorithms. The approach is suitable for standard systems...

The paper concerns a class of discounted restless bandit problems which possess an indexability property. Conservation laws yield an expression for the reward suboptimality of a general policy. These results are utilised to study the closeness to optimality of an index policy for a special class of simple and natural dual speed restless bandits for which indexability is guaranteed. The strong p...

We discuss the classical efficiency criteria in density estimation and propose some variants. The context is a general density estimation scheme that contains the cases of i.i.d. or dependent random variables, in discrete or continuous time. Unbiased estimation, optimality and asymptotic optimality are considered. An example of a density estimator that satisfies some suggested criteria is given...

Abstract. The article is devoted to second order optimality in Markov decision processes. Attention is primarily focused on the reward variance for discounted models and undiscounted transient models (i.e. where the spectral radius of the transition probability matrix is less then unity). Considering the second order optimality criteria means that in the class of policies maximizing (or minimiz...

Preemptively scheduling a set of independent jobs with release time on one processor is a historical problem. In this paper, the same problem has been considered in which objective is to minimize the mean flow time. To prepare a perfect branch-and-bound, some optimality conditions have been represented and they have been compared with the optimality conditions which have been proposed before. O...