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10 papers · 2 filters
Scalable Semidefinite Programming
Alp Yurtsever, Joel A. Tropp, Olivier Fercoq +2
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct ra…
On the convergence of stochastic primal-dual hybrid gradient
Ahmet Alacaoglu, Olivier Fercoq, Volkan Cevher
In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure co…
UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization
Ali Kavis, Kfir Y. Levy, Francis Bach +1
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simult…
A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators
Volkan Cevher, Bang Cong Vu
The proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}. Both methods were proposed for solving th…
An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints
Mehmet Fatih Sahin, Armin Eftekhari, Ahmet Alacaoglu +2
We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our metho…
Inertial Three-Operator Splitting Method and Applications
Volkan Cevher, Bang Cong Vu, Alp Yurtsever
We introduce an inertial variant of the forward-Douglas-Rachford splitting and analyze its convergence. We specify an instance of the proposed method to the three-composite convex…
An Optimal-Storage Approach to Semidefinite Programming using Approximate Complementarity
Lijun Ding, Alp Yurtsever, Volkan Cevher +2
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly con…
Almost surely constrained convex optimization
Olivier Fercoq, Ahmet Alacaoglu, Ion Necoara +1
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need t…
A Conditional Gradient-Based Augmented Lagrangian Framework
Alp Yurtsever, Olivier Fercoq, Volkan Cevher
This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing cond…
Stochastic Frank-Wolfe for Composite Convex Minimization
Francesco Locatello, Alp Yurtsever, Olivier Fercoq +1
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 so…