Publications de Quoc Tran Dinh

A Newton Frank-Wolfe method for constrained self-concordant minimization

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

SPRINGER2022

An adaptive primal-dual framework for nonsmooth convex minimization

Volkan Cevher, Quoc Tran Dinh, Ahmet Alacaoglu

We propose a new self-adaptive and double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov’s smoothing technique via general Bregman distance functions. It self-adaptiv ...

2020

Chemical machine learning with kernels: The impact of loss functions

Volkan Cevher, Quoc Tran Dinh, Sandip De, Van Quang Nguyen, Junhong Lin

Machine learning promises to accelerate materials discovery by allowing computational efficient property predictions from a small number of reference calculations. As a result, the literature has spent a considerable effort in designing representations tha ...

2019

A single-phase, proximal path-following framework

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

We propose a new proximal, path-following framework for a class of---possibly non-smooth---constrained convex problems. We consider settings where the non-smooth part is endowed with a proximity operator, and the constraint set is equipped with a self-conc ...

INFORMS2018

A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

Volkan Cevher, Quoc Tran Dinh

We propose a new and low per-iteration complexity first-order primal-dual optimization framework for a convex optimization template with broad applications. Our analysis relies on a novel combination of three classic ideas applied to the primal-dual gap fu ...

SIAM2018

Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization

Volkan Cevher, Quoc Tran Dinh, Ahmet Alacaoglu

We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied to the primal-dual gap function: smoothing, acceleration, homotopy, and coord ...

2017

Frank-Wolfe Works for Non-Lipschitz Continuous Gradient Objectives: Scalable Poisson Phase Retrieval

Volkan Cevher, Marwa El Halabi, Yen-Huan Li, Quoc Tran Dinh, Alp Yurtsever, Ya-Ping Hsieh, Gergely Odor

We study a phase retrieval problem in the Poisson noise model. Motivated by the PhaseLift approach, we approximate the maximum-likelihood estimator by solving a convex program with a nuclear norm constraint. While the Frank-Wolfe algorithm, together with t ...

Ieee2016

Convex block-sparse linear regression with expanders - provably

Volkan Cevher, Anastasios Kyrillidis, Luca Baldassarre, Bubacarr Bah, Quoc Tran Dinh

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-ti ...

2016

Composite convex minimization involving self-concordant-like cost functions

Volkan Cevher, Yen-Huan Li, Quoc Tran Dinh

The self-concordant-like property of a smooth convex func- tion is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofor ...

2015

A Primal-dual Framework For Mixtures Of Regularisers

Volkan Cevher, Baran Gözcü, Cosimo Aprile, Luca Baldassarre, Quoc Tran Dinh

Effectively solving many inverse problems in engineering requires to leverage all possible prior information about the structure of the signal to be estimated. This often leads to tackling constrained optimization problems with mixtures of regularizers. Pr ...

2015

Composite Self-Concordant Minimization

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying o ...

Massachusetts Institute of Technology Press2015

Composite convex minimization involving self-concordant-like cost functions

Volkan Cevher, Yen-Huan Li, Quoc Tran Dinh

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofore ...

2015

A Universal Primal-Dual Convex Optimization Framework

Volkan Cevher, Quoc Tran Dinh, Alp Yurtsever

We propose a new primal-dual algorithmic framework for a prototypical con- strained convex optimization template. The algorithmic instances of our frame- work are universal since they can automatically adapt to the unknown Ho ̈lder con- tinuity properties ...

2015

Learning with tensors: a framework based on convex optimization and spectral regularization

Quoc Tran Dinh

We present a framework based on convex optimization and spectral regularization to perform learning when feature observations are multidimensional arrays (tensors). We give a mathematical characterization of spectral penalties for tensors and analyze a uni ...

Springer2014

Barrier Smoothing for Nonsmooth Convex Minimization

Volkan Cevher, Yen-Huan Li, Quoc Tran Dinh

This paper proposes a smoothing technique for nonsmooth convex minimization using self-concordant barriers. To illustrate the main ideas, we compare our technique and the proximity smoothing approach (Nesterov2005) via the classical gradient method on both ...

Ieee2014

Constrained convex minimization via model-based excessive gap

Volkan Cevher, Quoc Tran Dinh

We introduce a model-based excessive gap technique to analyze first-order primal- dual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal fe ...

2014

Scalable sparse covariance estimation via self-concordance

Volkan Cevher, Anastasios Kyrillidis, Rabeeh Karimi Mahabadi, Quoc Tran Dinh

We consider the class of convex minimization problems, composed of a self-concordant function, such as the logdet metric, a convex data fidelity term h and, a regularizing -- possibly non-smooth -- function g. This type of problems have recently attracted ...

2014

An inexact proximal path-following algorithm for constrained convex minimization

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a ...

Siam Publications2014

Path-following gradient-based decomposition algorithms for separable convex optimization

Quoc Tran Dinh

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require ...

Springer Verlag2014

A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadra ...

2013