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

Decomposition Strategies for Nonconvex Problems, a Parametric Approach

This thesis deals with the development of numerical methods for solving nonconvex optimisation problems by means of decomposition and continuation techniques. We first introduce a novel decomposition algorithm based on alternating gradient projections and ...

EPFL2016

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Daniel Kressner

A novel method for approximating structured singular values (also known as

\mu

- values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eig ...

MATHICSE2016

MATHICSE Technical Report : A fast gradient method for nonnegative sparse regression with self dictionary

Robert Gerhard Jérôme Luce

Nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the input data matrix belong to the convex cone generated by only a few of its columns. The provably most robust met ...

MATHICSE2016

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

Composite Self-Concordant Minimization

Volkan Cevher, Quoc Tran Dinh, Anastasios Kyrillidis

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

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

Scalable sparse covariance estimation via self-concordance

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

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

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

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Volkan Cevher, Anastasios Kyrillidis

The convex l(1)-regularized log det divergence criterion has been shown to produce theoretically consistent graph learning. However, this objective function is challenging since the l(1)-regularization is nonsmooth, the log det objective is not globally Li ...

IEEE2013

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

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Decomposition Strategies for Nonconvex Problems, a Parametric Approach

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

MATHICSE Technical Report : A fast gradient method for nonnegative sparse regression with self dictionary

Composite convex minimization involving self-concordant-like cost functions

Composite convex minimization involving self-concordant-like cost functions

Composite Self-Concordant Minimization

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

Scalable sparse covariance estimation via self-concordance

Barrier Smoothing for Nonsmooth Convex Minimization

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Decomposition Strategies for Nonconvex Problems, a Parametric Approach

MATHICSE Technical Report : A novel iterative method to approximate structured singular values

Composite Self-Concordant Minimization

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

Composite convex minimization involving self-concordant-like cost functions

MATHICSE Technical Report : A fast gradient method for nonnegative sparse regression with self dictionary

Composite convex minimization involving self-concordant-like cost functions

Scalable sparse covariance estimation via self-concordance

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

Barrier Smoothing for Nonsmooth Convex Minimization