Publications by Quoc Tran Dinh

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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 ...

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 ...

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 ...

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived prev ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Quoc Tran Dinh

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

Convex block-sparse linear regression with expanders - provably

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

Time-Optimal Path Following for Robots With Convex-Concave Constraints Using Sequential Convex Programming

An inexact proximal path-following algorithm for constrained convex minimization

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

A Primal-dual Framework For Mixtures Of Regularisers

Composite convex minimization involving self-concordant-like cost functions

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

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

Scalable sparse covariance estimation via self-concordance

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

Constrained convex minimization via model-based excessive gap

A Universal Primal-Dual Convex Optimization Framework

Composite Self-Concordant Minimization

Barrier Smoothing for Nonsmooth Convex Minimization

Composite convex minimization involving self-concordant-like cost functions

An adaptive primal-dual framework for nonsmooth convex minimization

A single-phase, proximal path-following framework