Gevers M., Bombois X., Scorletti G., Van den Hof P., Hildebrand R. Experiment Design for Robust Control: Why Do More Work Than Is Needed? In Bruce A. Francis, Malcolm C. Smith, Jan C. Willems Eds.

Hildebrand R. Abstract cones of positive polynomials and their sums of squares relaxations. In Recent Advances in Optimization and its Applications in Engineering: The 14th Belgian-French-German Conference on Optimization, pp.41-50, Springer, Berlin, Heidelberg, 2010.

Hildebrand R. Classification of phase portraits of optimal synthesis.

Zelikin M.I., Zelikina L.F., Hildebrand R. Asymptotics of optimal synthesis for one class of extremal problems.

Zelikin M.I., Hildebrand R., Melnikov N.B. Topological structure of a typical fibre of optimal synthesis for chattering problems.

Hildebrand R., Gevers M. Identification for control: optimal input design with respect to a worst-case v-gap cost function.

Hildebrand R.

Hildebrand R. An Open Problem of Optimal Control Theory.

Hildebrand R. On the Number of Independent Control Sequences in the Symmetric Fuller Problem with Two-Dimensional Control.

Hildebrand R., Gevers M. Quantification of the variance of estimated transfer functions in the presence of undermodeling.

Hildebrand R., Lecchini A., Solari G., Gevers M. Prefiltering in Iterative Feedback Tuning: optimization of the prefilter for accuracy.

Hildebrand R., Lecchini A., Solari G., Gevers M. Asymptotic Accuracy of Iterative Feedback Tuning.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimal Prefiltering in Iterative Feedback Tuning.

Bombois X., Scorletti G., Gevers M., Hildebrand R., Van Den Hof P. Least costly identification experiment for control.

Hildebrand R. On the approximation of convex functions with cumulant generating functions.

Hildebrand R., Solari G. Identification for control: optimal input intended to identify a minimum variance controller.

Hildebrand R. Entangled states close to the maximally mixed state.

Hildebrand R. Exactness of sums of squares relaxations involving 3x3 matrices and Lorentz cones.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps.

Hildebrand R. Positive maps of second-order cones.

Hildebrand R. Concurrence revisited.

Hildebrand R. Positive partial transpose from spectra.

Poncet P., Hildebrand R., Cottet G.-H., Koumoutsakos P. Spatially distributed control for optimal drag reduction in cylinder wakes.

Hildebrand R., Mancini S., Severini S. Combinatorial Laplacians and Positivity Under Partial Transpose.

Hildebrand R. Semidefinite descriptions of low-dimensional separable matrix cones.

Gevers M., Bombois X., Hildebrand R., Solari G. Optimal Experiment Design for Open and Closed-loop System Identification.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps II.

Hildebrand R. Barriers on projective convex sets.

Hildebrand R. Half-dimensional immersions in para-Kähler manifolds.

Hildebrand R. The cross-ratio manifold: a model of centro-affine geometry.

Hildebrand R. The extreme rays of the 5 x 5 copositive cone.

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Geometry of neighbourhoods of singular extremals in problems with multi-dimensional control.

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems.

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Stochastic dynamics of Lie algebras of Poisson brackets in neighborhoods of nonsmoothness points of Hamiltonians.

Dickinson P.J.C., Dür M., Gijben L., Hildebrand R. Irreducible elements of the copositive cone.

Hildebrand R. On the infinity-norm of the cubic form of complete hyperbolic affine hyperspheres.

Hildebrand R. A lower bound on the barrier parameter of barriers for convex cones.

Dickinson P.J.C., Dür M., Gijben L., Hildebrand R. Scaling relationship between the copositive cone and Parrilo's first level approximation.

Hildebrand R. Hessian potentials with parallel derivatives.

Hildebrand R. Minimal zeros of copositive matrices.

Hildebrand R. Canonical barriers on convex cones.

Hildebrand R. Analytic formulas for complete hyperbolic affine spheres.

Hildebrand R., Gevers M., Solari G. Closed-loop Optimal Experiment Design: Solution via Moment Extension.

Hildebrand R. Centro-affine hypersurface immersions with parallel cubic form.

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Typicalness of chaotic fractal behaviour of integral vortices in Hamiltonian systems with discontinuous right hand side.

Hildebrand R. Spectrahedral cones generated by rank 1 matrices.

Dickinson P.J.C., Hildebrand R. Considering copositivity locally.

Hildebrand R. Copositive matrices with circulant zero support set.

Hildebrand R. Extremal copositive matrices with zero supports of cardinality n-2.

Hildebrand R. Extremal copositive matrices with minimal zero supports of cardinality two.

Belomestny D., Hildebrand R., Schoenmakers J. Optimal stopping via pathwise dual empirical maximisation.

Hildebrand R. Natural parametrizations of closed projective plane curves.

Hildebrand R. On the algebraic structure of the copositive cone.

Hildebrand R. Graph immersions with parallel cubic form.

Afonin A., Hildebrand R., Dickinson P.J.C. The extreme rays of the 6x6 copositive cone.

Hildebrand R. Optimal inequalities between distances in convex projective domains. Published online in

Hildebrand R. Linear group representations in the service of conic optimization. Plenary lecture at

Hildebrand R. Lower bounds on the barrier parameter of convex cones. Invited talk at

Hildebrand R., Dickinson P.J.C., Dür M., Gijben L. On the structure of the 5x5 copositive cone. Invited talk at

Hildebrand R. Geometric Aspects of Barriers for 3-Dimensional Cones. Invited talk at

Hildebrand R. Scaling points and reach for non-self-scaled barriers. Invited talk at

Hildebrand R. Geometry of self-concordant barriers. Mini-course at Summer School

Hildebrand R., Gevers M. Quantification of the variance of estimated transfer functions in the presence of undermodeling.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimal Prefiltering in Iterative Feedback Tuning.

Hildebrand R., Gevers M. Minimizing the worst-case v-gap by optimal input design.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimization of the prefilter in iterative feedback tuning for improved accuracy of the controller parameter update.

Hildebrand R., Gevers M. Identification for control: optimal input design with respect to a worst-case v-gap cost function.

Bombois X., Scorletti G., Van den Hof P., Gevers M., Hildebrand R. Least costly identification experiment for control. Proc.

Bombois X., Scorletti G., Gevers M., Hildebrand R., Van den Hof P. Cheapest open-loop identification for control.

Hildebrand R. Self-similar trajectories in multi-input systems.

Hildebrand R. A control problem with a Smale's Horseshoe in the solution.

Hildebrand R. Optimal inputs for FIR system identification.

Hildebrand R., Solari G. Closed-loop Optimal Input Design: the Partial Correlation Approach.

Rojas C.R., Hjalmarsson H., Hildebrand R. MIMO experiment design based on asymptotic model order theory.

Hildebrand R., Gevers M., Solari G. Closed-loop optimal experiment design: The partial correlation approach.

Rojas C.R., Katselis D., Hjalmarsson H., Hildebrand R., Bengtsson M. Chance constrained input design.

Despréaux S., Hildebrand R., Maignan A. Graph algorithm for the simulation of the interaction between particles.

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Generic fractal structure of the optimal synthesis in problems with affine multidimensional control.

Hildebrand R., Gevers M. Central extensions in closed-loop optimal experiment design.

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Typicalness of chaotic fractal behaviour of integral vortices in Hamiltonian systems with discontinuous right-hand side.

Hildebrand R. Optimal synthesis of controlled systems near a focus.

Hildebrand R. Classification of optimal syntheses of controlled systems near a focus.

Hildebrand R. A family of semidefinite relaxations for cones of positive polynomials.

Hildebrand R. A Geometric Theory of Barriers in Conic Optimization.

Hildebrand R. Semidefinite representations of sets delineated by plane quartics.

Hildebrand R. A barrier on convex cones with parameter equal to the dimension.

Gijben L., Dickinson P.J.C., Dür M., Hildebrand R. Scaling relationship between the copositive cone and Parrilo's first level approximation.

Ninin J., Hildebrand R. Abstract cones of positive polynomials and sums of squares.

Hildebrand R. Convex projective programming.

Gijben L., Dickinson P.J.C., Dür M., Hildebrand R. Scaling relationships between the copositive cone and the cone of sums of squares polynomials.

Girard A., Lebeaut P., Hildebrand R., Peltier N., Kaiser S. MaiMoSiNE / DOCEA Power: Assessing the quality of reduced order models of heat transfer in electronic devices.

Cottet G.-H., Hildebrand R., Koumoutsakos P., Mimeau C., Mortazavi I., Poncet P. Passive and active flow control using vortex methods.

Hildebrand R. Periodic discrete dynamical systems and copositive matrices with circulant zero patterns.

Hildebrand R. Barriers on symmetric cones.

Hildebrand R. Barriers on symmetric cones.

Hildebrand R. Parallelism conditions and algebras in affine differential geometry.

Hildebrand R. Extremal copositive matrices with zero supports of cardinality n-2.

Hildebrand R. Scaling points and reach for non-self-scaled barriers.

Hildebrand R. Self-associated three-dimensional cones.

Hildebrand R. Towards optimal barriers for convex cones.

Henrion R., Hildebrand R. Optimization in different flavors.

Hildebrand R. Introduction en optimisation convexe. Conférence

Hildebrand R. Exactness of the PPT condition for 3x3 matrices and approximation of convex functions with cumulant generating functions.

Hildebrand R. Exactness of the PPT condition for 3x3 matrices. Seminar of the Dept. of Mathematics, Drexel university, Philadelphia, USA, March 2005.

Hildebrand R., Solari G. Input design for the identification of a minimum variance controller.

Hildebrand R. Comparison of the PPT cone and the separable cone for 2 x n systems. Mathematical Programming seminar, CORE, UCL, Louvain-la-Neuve, Belgium, 2005. (slides)

Hildebrand R. Semidefinite description of separable cones involving the Lorentz cone.

Hildebrand R. Robust conic quadratic programming with ellipsoidal uncertainties. Seminar of the Automatic Control Group, School of Electrical Engineering, KTH, Stockholm, Sweden, November 2008. (slides)

Hildebrand R., Joncour I. Un système complexe astrophysique. Rencontres Nationales des Systèmes Complexes 2011, Roscoff, France, May 2011. (slides)

Hildebrand R. Abstract cones of positive polynomials and their sums of squares relaxations. Seminar Institut de Recherche Mathématiques de Rennes (IRMAR), Rennes, France, 2011. (slides)

Hildebrand R. Centro-affine differential geometry, Lagrangian submanifolds of the reduced paracomplex projective space, and conic optimization.

Hildebrand R. A partial differential equation characterizing determinants of symmetric cones.

Hildebrand R. Hessian potentials with parallel derivatives. Mathematical Programming seminar, CORE, UCL, Louvain-la-Neuve, Belgium, 2012. (slides)

Hildebrand R. Spectrahedral cones generated by rank 1 matrices.

Hildebrand R. Minimal zeros of copositive matrices. Dept. of Statistics and Operations Research, University of Vienna, Vienna, Austria, November 2014. (slides)

Hildebrand R. Rank 1 generated spectrahedral cones.

Hildebrand R. Extreme copositive matrices and periodic dynamical systems.

Hildebrand R. Canonical barriers on regular convex cones. Oberseminar Geometrische Analysis, Faculty of Mathematics, Goethe-Universität, Frankfurt a.M., Germany, April 2016. (slides)

Hildebrand R. Canonical barriers on regular convex cones. Rencontres ANR MAGA, IHES, Bures-sur-Yvette, France, December 2016. (slides)

Hildebrand R. Element-wise functions preserving positivity of matrices. Kolloquium Graduiertenkolleg ALOP, Univ. Trier, Germany, January 2017. (slides)

Hildebrand R. Extremal copositive matrices: approach via zero support sets.

Hildebrand R. Conic optimization: affine geometry of self-concordant barriers. Seminar Nonlinear Analysis and Optimization, Laboratoire de Mathèmatiques d'Avignon, France, April 2018. (slides)

Hildebrand R. On an optimal control problem with application to self-concordant barriers on convex cones. Seminar Geometric Theory of Optimal Control, Dept. of Mechanics and Mathematics, Moscow State University, Russia, April 2019. (website)

Hildebrand R. Conic optimization and self-concordant barriers. Mathematical Workshop of the School of Applied Mathematics and Computer Science, Russia, April 2019. (abstract)

Hildebrand R., Zelikin M.I., Lokutsievskiy L.V. Two-dimensional analog of the Fuller problem with control in a disk. Seminar Geometric Theory of Optimal Control, Dept. of Mechanics and Mathematics, Moscow State University, Russia, November 2019. (website,slides)

Afonin A., Hildebrand R., Dickinson P. The extreme rays of the 6x6 copositive cone. RICAM Special Semester workshop Conic and Copositive Optimization, Linz, Austria, December 2019. (slides)

Hildebrand R. On the convexity properties of the barrier parameter in conic programming. RICAM Special Semester workshop Conic and Copositive Optimization, Linz, Austria, December 2019. (slides)

Hildebrand R. Optimal step of the Newton method for self-concordant functions. Seminar Geometric Theory of Optimal Control, Dept. of Mechanics and Mathematics, Moscow State University, Russia, March 2020. (website,slides)

Hildebrand R. Projectively self-concordant barriers on convex sets. Submitted to

Frezat H., Hildebrand R., Maignan A. Simulation of hierarchical n-body systems based on dynamical trees. Submitted to

Hildebrand R. Optimal step length for the Newton method: case of self-concordant functions. Submitted to

Hildebrand R. Self-associated three-dimensional cones. Submitted to

Hildebrand R. Semi-definite representations for sets of cubics on the 2-sphere. Submitted to

Vorontsova E., Hildebrand R., Gasnikov A., Stonyakin F.

Hildebrand R., Lecchini A., Solari G., Gevers M. A convergence theorem for Iterative Feedback Tuning. Technical Report 2003/17, CESAME, Louvain-la-Neuve, Belgium.

Hildebrand R. PPT from spectra. Preprint arXiv quant-ph/0502170, 2005.

Hildebrand R. Cones of ball-ball separable elements. Preprint arXiv quant-ph/0503194, 2005.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps. Preprint Optimization Online 2005/12/1260, 2005.

Hildebrand R. Separable balls around the maximally mixed state for a 3-qubit system. Preprint arXiv quant-ph/0601201, 2006.

Hildebrand R., Mancini S., Severini S. Combinatorial Laplacians and Positivity Under Partial Transpose. Preprint arXiv cs.CC/0607036, 2006.

Hildebrand R. Concurrence of Lorentz-positive maps. Preprint arXiv quant-ph/0612064, 2006.

Hildebrand R. Semidefinite descriptions of separable matrix cones. Preprint arXiv math.RA/0701571, 2007.

Hildebrand R. Entangled states close to the maximally mixed state. Preprint arXiv quant-ph/0702040, 2007.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps II. Preprint Optimization Online 2007/08/1747, 2007.

Hildebrand R. Identification of community structure in networks with convex optimization. Preprint arXiv 0806.1896 [physics.data-an], 2008.

Hildebrand R. The extreme rays of the 5x5 copositive cone. Preprint Optimization Online 2011/03/2959, 2011.

Hildebrand R. A lower bound on the optimal self-concordance parameter of convex cones. Preprint Optimization Online 2011/06/3068, 2011.

Dickinson P., Dür M., Gijben L., Hildebrand R. Irreducible elements of the copositive cone. Preprint Optimization Online 2012/03/3383, 2012.

Dickinson P., Dür M., Gijben L., Hildebrand R. Scaling relationship between the copositive cone and Parrilo's first level approximation. Preprint Optimization Online 2012/03/3397, 2012.

Hildebrand R. Einstein-Hessian barriers on convex cones. Preprint Optimization Online 2012/05/3474, 2012.

Hildebrand R. Centro-affine hypersurface immersions with parallel cubic form. Preprint arXiv 1208.1155 [math.DG], 2012.

Hildebrand R. Graph immersions with parallel cubic form. Preprint arXiv 1302.1434 [math.DG], 2012.

Hildebrand R. Hessian potentials with parallel derivatives. Preprint arXiv 1303.7366 [math.DG], 2013.

Hildebrand R. Analytic formulas for complete hyperbolic affine spheres. Preprint arXiv 1305.4814 [math.DG], 2013.

Hildebrand R. Minimal zeros of copositive matrices. Preprint arXiv 1401.0134 [math.OC], 2014.

Dickinson P.J.C., Hildebrand R. Considering copositivity locally. Preprint Optimization Online 2014/04/4315, 2014.

Hildebrand R. Spectrahedral cones generated by rank 1 matrices. Mathematisches Forschungsinstitut Oberwolfach, Report No. 17/2014, pp. 53-56, 2014.

Hildebrand R. Spectrahedral cones generated by rank 1 matrices. Preprint arXiv 1409.4781 [math.OC], 2015.

Belomestny D., Hildebrand R., Schoenmakers J. Optimal stopping via path-wise dual empirical maximization. WIAS preprint 2043, 2014.

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Typicalness of chaotic fractal behaviour of integral vortices in Hamiltonian systems with discontinuous right hand side. Preprint arXiv 1506.02320 [math.DS], 2015.

Hildebrand R. Copositive matrices with circulant zero support set. Preprint arXiv 1603.05111 [math.OC], 2016.

Hildebrand R., Schoenmakers J., Zhang J., Dickmann F. Regression based duality approach to optimal control with application to hydro electricity storage. WIAS preprint 2330, 2016.

Hildebrand R. Extremal copositive matrices with minimal zero supports of cardinality two. Preprint arXiv 1707.08862 [math.OC], 2017.

Hildebrand R. Self-associated three-dimensional cones. Preprint arXiv 1806.06588 [math.DG], 2018.

Hildebrand R. Natural parametrizations of closed projective plane curves. Preprint arXiv 1810.06675 [math.DG], 2018.

Hildebrand R. Projectively self-concordant barriers on convex cones. Preprint arXiv 1909.01883 [math.OC], 2019.

Afonin A., Hildebrand R., Dickinson P. The extreme rays of the 6x6 copositive cone. Preprint Optimization Online 2019/11/7489, 2019.

Hildebrand R. On the algebraic structure of the copositive cone. Preprint Optimization Online 2020/01/7597, 2020.

Hildebrand R. Optimal step length for the Newton method near the minimum of a self-concordant function. Preprint arXiv 2003.08650 [math.OC], 2020.

Hildebrand R. Optimal inequalities between distances in convex projective domains. Preprint arXiv 2005.05867 [math.DG], 2020.

Hildebrand R., Afonin A. Essential components of extremal copositive matrices. Preprint hal 02571648, 2020.

Hildebrand R. Semi-definite representations for sets of cubics on the 2-sphere. Preprint arXiv 2103.13270 [math.OC], 2021.

Last modification: June 4, 2021