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- Peyman Mohajerin Esfahani, Tobias Sutter, John Lygeros
- IEEE Trans. Automat. Contr.
- 2015

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)

- Tobias Sutter, David Sutter, Peyman Mohajerin Esfahani, John Lygeros
- IEEE Transactions on Information Theory
- 2015

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<sup>2</sup> N√log N/ε) to provide an… (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)

- David Sutter, Tobias Sutter, Peyman Mohajerin Esfahani, Renato Renner
- IEEE Transactions on Information Theory
- 2016

We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite-dimensional output 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 additive ε-close estimate… (More)

- Tobias Sutter, Arnab Ganguly, Heinz Koeppl
- ArXiv
- 2015

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)

- David Sutter, Peyman Mohajerin Esfahani, Tobias Sutter, John Lygeros
- 2014 IEEE International Symposium on Information…
- 2014

We propose an iterative method for efficiently approximating the capacity of discrete memoryless channels, possibly having additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To find an ε-approximation of the capacity, in case of no additional input… (More)

- Tobias Sutter, Peyman Mohajerin Esfahani, David Sutter, John Lygeros
- 2014 IEEE International Symposium on Information…
- 2014

We present a new algorithm, based on duality of convex programming and the specific structure of the channel capacity problem, to iteratively construct upper and lower bounds for the capacity of memoryless channels having continuous input and countable output alphabets. Under a mild assumption on the decay rate of the channel's tail, explicit bounds for the… (More)

— We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure space and prove equivalence of the two formulations under mild assumptions, significantly weaker than those found in… (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)