Publications associées à A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

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

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

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

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

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

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

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

Stochastic Frank-Wolfe for Composite Convex Minimization

Volkan Cevher, Alp Yurtsever

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...

2019

Sampling can be faster than optimization

Nicolas Henri Bernard Flammarion

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...

PNAS2019

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

Pierino Lestuzzi, Lorenzo Diana

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8 (EC8). However, a lack of accuracy of the N2 method in certain conditio ...

2019

A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

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Mathematical Foundations of Robust and Distributionally Robust Optimization

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

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

Convex optimization in sums of Banach spaces

Convergence of adaptive algorithms for constrained weakly convex optimization

Scalable Semidefinite Programming

Implications of ANEC for SCFTs in four dimensions

Stochastic Frank-Wolfe for Composite Convex Minimization

Sampling can be faster than optimization

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

Implications of ANEC for SCFTs in four dimensions

Convergence of adaptive algorithms for constrained weakly convex optimization

Stochastic Frank-Wolfe for Composite Convex Minimization

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

Mathematical Foundations of Robust and Distributionally Robust Optimization

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

Sampling can be faster than optimization

Convex optimization in sums of Banach spaces

Scalable Semidefinite Programming

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method