Publications related to Stochastic Frank-Wolfe for Composite Convex Minimization

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

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

Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates

Martin Jaggi, Sebastian Urban Stich, Amirkeivan Mohtashami

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and—in asynchronous implementations—on the gradient staleness. Especially, it has been observed that the spe ...

2021

An Optimal-Storage Approach to Semidefinite Programming Using Approximate Complementarity

Volkan Cevher, Alp Yurtsever

This paper develops a new storage-optimal algorithm that provably solves almost all semidefinite programs (SDPs). This method is particularly effective for weakly constrained SDPs under appropriate regularity conditions. The key idea is to formulate an app ...

SIAM PUBLICATIONS2021

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

Form-finding of tensegrity structures via rank minimization of force density matrix

Yafeng Wang

This study proposes a general computational framework for the form-finding of tensegrity structures. The procedure is divided into two stages in which the member force densities and nodal coordinates are obtained respectively. In the first stage, the deter ...

ELSEVIER SCI LTD2021

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

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

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Stochastic Frank-Wolfe for Composite Convex Minimization

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

Convex optimization in sums of Banach spaces

Mathematical Foundations of Robust and Distributionally Robust Optimization

Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates

An Optimal-Storage Approach to Semidefinite Programming Using Approximate Complementarity

Convergence of adaptive algorithms for constrained weakly convex optimization

Form-finding of tensegrity structures via rank minimization of force density matrix

Implications of ANEC for SCFTs in four dimensions

Scalable Semidefinite Programming

Adaptive Gradient Descent without Descent

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

Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates

An Optimal-Storage Approach to Semidefinite Programming Using Approximate Complementarity

Mathematical Foundations of Robust and Distributionally Robust Optimization

Scalable Semidefinite Programming

Adaptive Gradient Descent without Descent

Convex optimization in sums of Banach spaces

Form-finding of tensegrity structures via rank minimization of force density matrix

Convergence of adaptive algorithms for constrained weakly convex optimization

Implications of ANEC for SCFTs in four dimensions