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Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…
For memoryless channels with continuous input alphabets, deterministic identification (DI) typically exhibits a linearithmic ($n\log n$) message growth. However, the exact DI capacity has long remained open due to a persistent gap between…
New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the "smooth 0-divergence", which is a generalization of Renyi's divergence of order…
In this paper, we derive upper and lower bounds as well as a simple closed-form approximation for the capacity of the continuous-time, bandlimited, additive white Gaussian noise channel in a three-dimensional free-space electromagnetic…
We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…
We derive improved and easily computable upper bounds on the capacity of the discrete-time Poisson channel under an average-power constraint and an arbitrary constant dark current term. This is accomplished by combining a general convex…
Current advancements in communication equipment demand the investigation of classical information transfer over quantum channels, by encompassing realistic scenarios in finite dimensions. To address this issue, we develop a framework for…
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
We develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functionals, we introduce closed convex processes -- set-valued…
A discrete compound channel with memory is considered, where no stationarity, ergodicity or information stability is required, and where the uncertainty set can be arbitrary. When the discrete noise is additive but otherwise arbitrary and…
In this paper we present a foundational study on a constrained method that defines learning problems with Neural Networks in the context of the principle of least cognitive action, which very much resembles the principle of least action in…
The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the…
The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the $(1,\infty)$-RLL constraint. We derive the capacity for this setting, which can be…
In this paper we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC program in which the first convex component of the objective and constraints is the sum of a smooth and nonsmooth functions while their…
A practical communication channel often suffers from constraints on input other than the average power, such as the peak power constraint. In order to compare achievable rates with different constellations as well as the channel capacity…