Publications related to Real analysis

A first-order primal-dual method with adaptivity to local smoothness

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

2021

On the Equivalence of Youla, System-Level, and Input-Output Parameterizations

Maryam Kamgarpour, Luca Furieri, Yu Zheng

A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doubly coprime factorization of the system, while the recent system-level and input-o ...

2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Mathematical Foundations of Robust and Distributionally Robust Optimization

Daniel Kuhn, Jianzhe Zhen, Wolfram Wiesemann

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambigu ...

2021

Reactive Navigation in Crowds for Non-holonomic Robots with Convex Bounding Shape

Aude Billard, Diego Felipe Paez Granados, David Julian Gonon

This paper describes a novel method for non-holonomic robots of convex shape to avoid imminent collisions with moving obstacles. The method's purpose is to assist navigation in crowds by correcting steering from the robot's path planner or driver. We evalu ...

2021

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Vincent Gramoli

There is an increasing interest in a fast-growing machine learning technique called Federated Learning (FL), in which the model training is distributed over mobile user equipment (UEs), exploiting UEs' local computation and training data. Despite its advan ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Deep Boltzmann Machines: Rigorous Results at Arbitrary Depth

Emanuele Mingione, Diego Alberici

A class of deep Boltzmann machines is considered in the simplified framework of a quenched system with Gaussian noise and independent entries. The quenched pressure of a K-layers spin glass model is studied allowing interactions only among consecutive laye ...

2021

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Ahmet Alacaoglu

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

EPFL2021

Fast Projection Onto Convex Smooth Constraints

Maryam Kamgarpour, Andreas Krause, Ilnura Usmanova

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where ...

PMLR2021

Stabilization and Accuracy Improvement of Power-Hardware-in-the-Loop Test Using a Robust Data-Driven Method

Alireza Karimi, Seyed Sohail Madani

Power-Hardware-In-the-Loop (PHIL) setups have gained high importance in validation of the performance of newly developed algorithms and devices with low risk and implementation cost. However, the interconnection of a power hardware with a simulated model v ...

2021

Real analysis

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A first-order primal-dual method with adaptivity to local smoothness

On the Equivalence of Youla, System-Level, and Input-Output Parameterizations

Convex optimization in sums of Banach spaces

Mathematical Foundations of Robust and Distributionally Robust Optimization

Reactive Navigation in Crowds for Non-holonomic Robots with Convex Bounding Shape

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Deep Boltzmann Machines: Rigorous Results at Arbitrary Depth

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Fast Projection Onto Convex Smooth Constraints

Stabilization and Accuracy Improvement of Power-Hardware-in-the-Loop Test Using a Robust Data-Driven Method

Convex optimization in sums of Banach spaces

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Reactive Navigation in Crowds for Non-holonomic Robots with Convex Bounding Shape

A first-order primal-dual method with adaptivity to local smoothness

On the Equivalence of Youla, System-Level, and Input-Output Parameterizations

Mathematical Foundations of Robust and Distributionally Robust Optimization

Deep Boltzmann Machines: Rigorous Results at Arbitrary Depth

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Stabilization and Accuracy Improvement of Power-Hardware-in-the-Loop Test Using a Robust Data-Driven Method

Fast Projection Onto Convex Smooth Constraints