We consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables. This class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs. Examples include infinite horizon production planning under time-varying demands and equipment replacement under t...

Under the assumption that δ is a Woodin cardinal and GCH holds, I show that if F is any class function from the regular cardinals to the cardinals such that (1) κ < cf(F (κ)), (2) κ < λ implies F (κ) ≤ F (λ), and (3) δ is closed under F , then there is a cofinality-preserving forcing extension in which 2 = F (γ) for each regular cardinal γ < δ, and in which δ remains Woodin. Unlike the analogou...

We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisf...

In the previous class, we had described a universal learning algorithm, called ERM (Empirical Risk Minimization). Under the ERM principle, we want to learn a function f , and we are promised that this function belongs to the function class H. We are given a training set S, and the ERM algorithm returns a function h ∈ H that minimizes the error on the training sample. That is, h = argming∈H errS...

In this paper the problem of robust control for a class of linear infinite dimensional systems under mixed disturbances of the multiplicative type is addressed. The Lyapunov function approach is used for proving that there is a controller that stabilizes this class of systems under the presence of uncertainties and perturbations, and guarantees some tolerance level for the joint cost functional...

A user generates $n$ independent and identically distributed data random variables with a probability mass function that must be guarded from querier. The querier recover, prescribed accuracy, given of the each query responses upon eliciting them user. chooses devises to maximize distribution privacy as gauged by (Kullback...