Publications related to Inclusions différentielles et problèmes variationnels

Approximate dynamic programming via sum of squares programming

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables. By rela ...

2013

Erdos-Szekeres-type theorems for monotone paths and convex bodies

János Pach

For any sequence of positive integers j(1)< j(2)= 2 and q >= 2, what is the s ...

London Math Soc2012

The Two-Well Problem For Piecewise-Affine Maps

Bernard Dacorogna

In the two-well problem we look for a map u which satisfies Dirichlet boundary conditions and whose gradient Du assumes values in SO (2) A boolean OR SO (2) B = S-A boolean OR S-B, for two given invertible matrices A, B (an element of SO (2) A is of the fo ...

2012

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Volkan Cevher, Anastasios Kyrillidis

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a well-known memory ...

IEEE2012

Fast hard thresholding with Nesterov's gradient method

Volkan Cevher, Sina Jafarpour

We provide an algorithmic framework for structured sparse recovery which unifies combinatorial optimization with the non-smooth convex optimization framework by Nesterov [1, 2]. Our algorithm, dubbed Nesterov iterative hard-thresholding (NIHT), is similar ...

2010

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Marc Troyanov

David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain

\Omega

in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of smoothness of t ...

2009

Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiently

Friedrich Eisenbrand

In this paper, we introduce the notion of a constrained Minkowski sum: for two (finite) point-sets P, Q subset of R-2 and a set of k inequalities Ax >= b, it is defined as the point-set (P circle plus Q)(Ax >= b) = {x = p + q vertical bar p is an element o ...

Springer-Verlag2009

A hybrid model predictive control scheme for multi-agent containment and distributed sensing

Giancarlo Ferrari Trecate

This paper deals with distributed sensing over a field by means of a multi-agent control architecture. A leader/follower scheme is built up for exploring an environment by properly sensing areas of interest. By means of a control architecture based on dece ...

2009

Extended Formulations for Packing and Partitioning Orbitopes

Yuri Faenza

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in Kaibel and Pfetsch [Kaibel, V., M. E. Pfetsch. 2008. Packing and partitioning orbitopes. Math. Programming ...

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

Inclusions différentielles et problèmes variationnels

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Approximate dynamic programming via sum of squares programming

Erdos-Szekeres-type theorems for monotone paths and convex bodies

The Two-Well Problem For Piecewise-Affine Maps

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Fast hard thresholding with Nesterov's gradient method

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiently

A hybrid model predictive control scheme for multi-agent containment and distributed sensing

Extended Formulations for Packing and Partitioning Orbitopes

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

Constrained Minkowski Sums: A Geometric Framework for Solving Interval Problems in Computational Biology Efficiently

A hybrid model predictive control scheme for multi-agent containment and distributed sensing

Erdos-Szekeres-type theorems for monotone paths and convex bodies

Approximate dynamic programming via sum of squares programming

Fast hard thresholding with Nesterov's gradient method

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Extended Formulations for Packing and Partitioning Orbitopes

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

The Two-Well Problem For Piecewise-Affine Maps

Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction