Publications related to Convex analysis

Convex optimization in sums of Banach spaces

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

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

Volkan Cevher, Maria-Luiza Vladarean

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

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

Convergence of adaptive algorithms for constrained weakly convex optimization

Volkan Cevher, Ahmet Alacaoglu, Yurii Malitskyi

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Ali H. Sayed, Sulaiman A S A E Alghunaim, Ming Yan

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...

IEEE2020

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

Maryam Kamgarpour

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADM ...

2020

Implications of ANEC for SCFTs in four dimensions

Andrea Manenti, Alessandro Vichi

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Delta of operators in four-dimensional N = 1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity ...

SPRINGER2020

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Shaul Nadav Hallak

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...

SPRINGER/PLENUM PUBLISHERS2020

Scalable Semidefinite Programming

Volkan Cevher, Alp Yurtsever

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct algorithm for solving large SDP problems by economizing on both the storage an ...

2020

Convex analysis

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Convex optimization in sums of Banach spaces

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

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

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Convergence of adaptive algorithms for constrained weakly convex optimization

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

Implications of ANEC for SCFTs in four dimensions

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Scalable Semidefinite Programming

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

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Implications of ANEC for SCFTs in four dimensions

Scalable Semidefinite Programming

Convex optimization in sums of Banach spaces

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

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Convergence of adaptive algorithms for constrained weakly convex optimization