Publications associées à Cône convexe

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

Optimal containment control for a class of heterogeneous multi-agent systems with actuator faults

Ju Wu, Tong Wang

This article investigates the optimal containment control problem for a class of heterogeneous multi-agent systems with time-varying actuator faults and unmatched disturbances based on adaptive dynamic programming. Since there exist unknown input signals i ...

WILEY2023

Invariant integrals on topological groups

Vasco Schiavo

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

The uniform symbolic topology property for diagonally F-regular algebras

Javier Alonso Carvajal Rojas

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...

2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Stochastic Frank-Wolfe for Composite Convex Minimization

Volkan Cevher, Alp Yurtsever

A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed fo ...

2019

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Robert Gerhard Jérôme Luce

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust met ...

Ieee-Inst Electrical Electronics Engineers Inc2018

The hamburger theorem

Jan Kyncl

We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...

Elsevier Science Bv2018

Generalized convex hull construction for materials discovery

Michele Ceriotti, Edgar Albert Engel, Andrea Anelli

Searching for novel materials involves identifying potential candidates and selecting those that have desirable properties and facile synthesis. It is relatively easy to generate large numbers of potential candidates, for instance, by computational searche ...

2018

Optical Tomography Based On A Nonlinear Model That Handles Multiple Scattering

Michaël Unser, Demetri Psaltis, Ulugbek Kamilov, Alexandre Goy, Joowon Lim

Learning Tomography (LT) is a nonlinear optimization algorithm for computationally imaging three-dimensional (3D) distribution of the refractive index in semi-transparent samples. Since the energy function in LT is generally non-convex, the solution it obt ...

Ieee2017

Moment-sum-of-squares hierarchies for set approximation and optimal control

Milan Korda

This thesis uses the idea of lifting (or embedding) a nonlinear controlled dynamical system into an infinite-dimensional space of measures where this system is equivalently described by a linear equation. This equation and problems involving it are subsequ ...

EPFL2016

Guaranteeing Input Tracking For Constrained Systems: Theory and Application to Demand Response

Colin Neil Jones, Tomasz Tadeusz Gorecki, Georgios Stathopoulos, Altug Bitlislioglu

A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination of its inputs. U ...

2015

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

Pierre Vandergheynst, Mahdad Hosseini Kamal

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensio ...

Springer-Verlag2015

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

Institute of Electrical and Electronics Engineers2014

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

Pierre Vandergheynst, Mahdad Hosseini Kamal

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensio ...

2014

On The Convergence Of The Affine Hull Of The Chvatal-Gomory Closures

Yuri Faenza, Marco Di Summa

Given an integral polyhedron P subset of R-n and a rational polyhedron Q subset of R-n containing the same integer points as P, we investigate how many iterations of the Chvatal-Gomory closure operator have to be performed on Q to obtain a polyhedron conta ...

SIAM Publications2013

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

2013

New Results in the Theory of Linear and Integer Programming

Nicolai Hähnle

The polynomial Hirsch conjecture states that the vertex-edge diameter of a d-dimensional polyhedron with n facets is bounded by a polynomial in d and n. For the special case where the polyhedron is defined as the set of points satisfying a system Ax ≤ b of ...

EPFL2012

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments ...

2008

Phase-sensitive Fourier space imaging of optical Bloch modes

Romuald Houdré, Nicolas Le Thomas

We present a phase-shifting holography method in k space that allows us to investigate the phase and amplitude of optical Bloch waves. The method is based on a Fourier space imaging technique combined with a Mach-Zehnder interferometer. Using a W3 photonic ...

2008