Publications related to A Global Existence Result for the Semigeostrophic Equations in Three Dimensional Convex Domains

Separation and Duality in Locally L0-Convex Modules

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

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

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

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non- convex set of stabilizing control ...

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

Robust Pole Placement of Systems with Polytopic Uncertainty Via Convex Optimization

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non-convex set of stabilizing controll ...

2007

Robust Control of Polytopic Systems by Convex Optimization

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional app ...

2007

Robust Control of Polytopic Systems by Convex Optimization

Alireza Karimi, Roland Longchamp, Hamid Khatibi

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional app ...

2007

Inclusions différentielles et problèmes variationnels

Ana Margarida Fernandes Ribeiro

In this thesis we deal with three different but connected questions. Firstly (cf. Chapter 2) we make a systematic study of the generalized notions of convexity for sets. We study the notions of polyconvex, quasiconvex and rank one convex set. We remark tha ...

EPFL2006

The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation

Jean-Yves Le Boudec, Milan Vojnovic

We define ``random trip", a generic mobility model for random, independent node motions, which contains as special cases: the random waypoint on convex or non convex domains, random walk on torus, billiards, city section, space graph, intercity and other m ...

2006

A Global Existence Result for the Semigeostrophic Equations in Three Dimensional Convex Domains

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Separation and Duality in Locally L0-Convex Modules

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

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

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Monotone and Cash-Invariant Convex Functions and Hulls

Robust Pole Placement of Systems with Polytopic Uncertainty Via Convex Optimization

Robust Control of Polytopic Systems by Convex Optimization

Robust Control of Polytopic Systems by Convex Optimization

Inclusions différentielles et problèmes variationnels

The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation

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

Monotone and Cash-Invariant Convex Functions and Hulls

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Inclusions différentielles et problèmes variationnels

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

Separation and Duality in Locally L0-Convex Modules

Robust Pole Placement of Systems with Polytopic Uncertainty Via Convex Optimization

Robust Control of Polytopic Systems by Convex Optimization

Robust Control of Polytopic Systems by Convex Optimization

The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation