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We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly(More)
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. The presented method requires O(M 2 N √ log N ε) to provide an estimate of the capacity(More)
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an ε-close estimate to the(More)
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the(More)
We consider discrete memoryless channels with input alphabet size n and output alphabet size m, where m = ⌈γn⌉ for some constant γ > 0. The channel transition matrix consists of entries that, before being normalized, are independent and identically distributed nonnega-tive random variables V and such that E (V log V) 2 < ∞. We prove that in the limit as n →(More)
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing(More)
The capacity of a quantum channel characterizes the ultimate rate at which information can be transmitted reliably over the channel. Its computation, however, turns out to be difficult. Here we introduce a framework that connects recent techniques from convex optimization with quantum information theoretic problems. It can be used to derive an iterative(More)
We consider discrete memoryless channels with input alphabet size n and output alphabet size m, where m = ⌈γn⌉ for some constant γ > 0. The channel transition matrix consists of entries that, before being normalised, are independent and identically distributed nonnega-tive random variables V and such that E (V log V) 2 < ∞. We prove that in the limit as n →(More)