Publications related to Convex optimization in sums of Banach spaces

Hypomonotonicity of the Normal Cone and Proximal Smoothness

We study the properties of the normal cone to a proximally smooth set. We give a complete characterization of a proximally smooth set through the monotonicity properties of its normal cone in an arbitrary uniformly convex and uniformly smooth Banach space. ...

Heldermann Verlag2017

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

In this paper, we consider the problem of sequentially optimizing a black-box function

f

based on noisy samples and bandit feedback. We assume that

f

is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yield ...

2017

New Moduli For Banach Spaces

Grigory Ivanov

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...

Tusi Mathematical Research Group2017

Lipschitz changes of variables between perturbations of log-concave measures

Maria Colombo

Extending a result of Caffarelli, we provide global Lipschitz changes of variables between compactly supported perturbations of log-concave measures. The result is based on a combination of ideas from optimal transportation theory and a new Pogorelov-type ...

2017

Partition function on spheres: How to use zeta function regularization

Alexander Monin

It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We c ...

Amer Physical Soc2016

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Volkan Cevher

This paper proposes a tradeoff between computational time, sample complexity, and statistical accuracy that applies to statistical estimators based on convex optimization. When we have a large amount of data, we can exploit excess samples to decrease stati ...

Ieee-Inst Electrical Electronics Engineers Inc2015

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography

Jean-Philippe Thiran, Alessandro Daducci, Alia Lemkaddem

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion MRI data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the ne ...

Institute of Electrical and Electronics Engineers2015

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In recent works, sparse models and convex optimization techniques have been applied to radio-interferometric (RI) imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. In this talk, I will review our latest contribut ...

2015

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

Maria Colombo

In this paper we make a survey of some recent developments of the theory of Sobolev spaces W-1,W-q (X, d, m), 1 < q < infinity, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev spac ...

2015

PURIFY: a new approach to radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a m ...

Wiley-Blackwell2014

Convex optimization in sums of Banach spaces

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Hypomonotonicity of the Normal Cone and Proximal Smoothness

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

New Moduli For Banach Spaces

Lipschitz changes of variables between perturbations of log-concave measures

Partition function on spheres: How to use zeta function regularization

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

PURIFY: a new approach to radio-interferometric imaging

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

Why CLEAN when you can PURIFY? A new approach for next-generation radio-interferometric imaging

COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography

Hypomonotonicity of the Normal Cone and Proximal Smoothness

PURIFY: a new approach to radio-interferometric imaging

Lipschitz changes of variables between perturbations of log-concave measures

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

Partition function on spheres: How to use zeta function regularization

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

New Moduli For Banach Spaces