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

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

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Composite convex minimization involving self-concordant-like cost functions

Volkan Cevher, Quoc Tran Dinh, Yen-Huan Li

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

Composite convex minimization involving self-concordant-like cost functions

Volkan Cevher, Quoc Tran Dinh, Yen-Huan Li

Abstract. 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 ...

2015

A Primal-dual Framework For Mixtures Of Regularisers

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

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

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

Volkan Cevher, Quoc Tran Dinh

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis techn ...

2014

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

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

Barrier Smoothing for Nonsmooth Convex Minimization

Volkan Cevher, Quoc Tran Dinh, Yen-Huan Li

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

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

Volkan Cevher, Quoc Tran Dinh, Anastasios Kyrillidis

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

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

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Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Composite convex minimization involving self-concordant-like cost functions

Composite convex minimization involving self-concordant-like cost functions

A Primal-dual Framework For Mixtures Of Regularisers

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

Constrained convex minimization via model-based excessive gap

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

Barrier Smoothing for Nonsmooth Convex Minimization

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

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

A Primal-dual Framework For Mixtures Of Regularisers

Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization

Composite convex minimization involving self-concordant-like cost functions

Composite convex minimization involving self-concordant-like cost functions

Constrained convex minimization via model-based excessive gap

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

Barrier Smoothing for Nonsmooth Convex Minimization

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

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