Publications related to Continuity Properties of Law-Invariant (Quasi-)Convex Risk Functions on L∞

To Convexify or Not? Regression with Clustering Penalties on Graphs

Volkan Cevher, Luca Baldassarre, Marwa El Halabi

We consider minimization problems that are compositions of convex functions of a vector

\x \in\reals^N

with submodular set functions of its support (i.e., indices of the non-zero coefficients of

\x

). Such problems are in general difficult for large

N

...

IEEE2013

A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Anna Auria Rasclosa

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bi-spectrum measurements. We formulate a linear version of the problem for the order-3 tensor formed by the tensor product of the ...

2013

Regularized Bundle Methods for Convex and Non-Convex Risks

Machine learning is most often cast as an optimization problem. Ideally, one expects a convex objective function to rely on efficient convex optimizers with nice guarantees such as no local optima. Yet, non-convexity is very frequent in practice and it may ...

2012

Approaches to Conditional Risk

Damir Filipovic

We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on Lp spaces, while the other approach utilizes module-based convex analysis wher ...

2012

An Optimal Algorithm for Reconstructing Images from Binary Measurements

Martin Vetterli, Luciano Sbaiz, Yue Lu, Feng Yang

We have studied a camera with a very large number of binary pixels referred to as the gigavision camera or the gigapixel digital film camera. Potential advantages of this new camera design include improved dynamic range, thanks to its logarithmic sensor re ...

2010

Minimum distance between pattern transformation manifolds: Algorithm and Applications

Pascal Frossard, Effrosyni Kokiopoulou

Transformation invariance is an important property in pattern recognition, where different observations of the same object typically receive the same label. This paper focuses on a transformation invariant distance measure that represents the minimum dista ...

2009

Separation and Duality in Locally L0-Convex Modules

Damir Filipovic

Motivated by financial applications, we study convex analysis for modules over the ordered ring L0 of random variables. We establish a module analogue of locally convex vector spaces, namely locally L0-convex modules. In this context, we prove hyperplane s ...

2009

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Bernard Dacorogna

Any finite, separately convex, positively homogeneous function on

\mathbb{R}^2

is convex. This was first established by the first author ["Direct methods in calculus of variations", Springer-Verlag (1989)]. Here we give a new and concise proof of this re ...

2008

Monotone and Cash-Invariant Convex Functions and Hulls

Damir Filipovic

This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to ...

2007

Perfect Simulation and Stationarity of a Class of Mobility Models

Jean-Yves Le Boudec, Milan Vojnovic

We define ``random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm ...

2005

Continuity Properties of Law-Invariant (Quasi-)Convex Risk Functions on L∞

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To Convexify or Not? Regression with Clustering Penalties on Graphs

A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

Regularized Bundle Methods for Convex and Non-Convex Risks

Approaches to Conditional Risk

An Optimal Algorithm for Reconstructing Images from Binary Measurements

Minimum distance between pattern transformation manifolds: Algorithm and Applications

Separation and Duality in Locally L0-Convex Modules

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Monotone and Cash-Invariant Convex Functions and Hulls

Perfect Simulation and Stationarity of a Class of Mobility Models

An Optimal Algorithm for Reconstructing Images from Binary Measurements

Separation and Duality in Locally L0-Convex Modules

Regularized Bundle Methods for Convex and Non-Convex Risks

Monotone and Cash-Invariant Convex Functions and Hulls

The role of perspective functions in convexity, polyconvexity, rank-one convexity and separate convexity

Perfect Simulation and Stationarity of a Class of Mobility Models

To Convexify or Not? Regression with Clustering Penalties on Graphs

Minimum distance between pattern transformation manifolds: Algorithm and Applications

A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

Approaches to Conditional Risk