Tobias Sutter

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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 ChanceConstrained 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<sup>2</sup> N&#x221A;log N/&#x03B5;) to provide an(More)
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 &#x03B5;-close estimate(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)
This paper considers discrete-time constrained Markov control processes (MCPs) under the long-run expected average cost optimality criterion. For Borel state and action spaces a two-step method is presented to numerically approximate the optimal value of this constrained MCPs. The proposed method employs the infinite-dimensional linear programming (LP)(More)
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 &#x03B5;-approximation of the capacity, in case of no additional input(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)
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 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(More)