Books

Vorontsova E., Hildebrand R., Gasnikov A., Stonyakin F. Convex Optimization. MIPT Press, Moscow, 2021 (in Russian). (preprint)


Book chapters

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. Control of Uncertain Systems: Modelling, Approximation, and Design: A Workshop on the Occasion of Keith Glover's 60th Birthday, Lecture Notes in Control and Information Sciences Vol. 329, pp. 139 - 162. Springer, Berlin, Heidelberg, 2006.

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.


Journals

Hildebrand R. Classification of phase portraits of optimal synthesis. Fundamental and Applied Mathematics, 7(1):199-233, 2001 (in Russian).

Zelikin M.I., Zelikina L.F., Hildebrand R. Asymptotics of optimal synthesis for one class of extremal problems. Proceedings of the Steklov Institute of Mathematics, 233:87-115, 2001 (Russian version).

Zelikin M.I., Hildebrand R., Melnikov N.B. Topological structure of a typical fibre of optimal synthesis for chattering problems. Proceedings of the Steklov Institute of Mathematics, 233:116-142, 2001 (Russian version).

Hildebrand R., Gevers M. Identification for control: optimal input design with respect to a worst-case v-gap cost function. SIAM Journal on Control and Optimization, 41(5):1586-1608, 2003.

Hildebrand R. Invariants in the Riemannian geometry of convex sets. CORE Discussion Paper 2004/7, abstract, 2004.

Hildebrand R. An Open Problem of Optimal Control Theory. Journal of Mathematical Sciences, 121(2):2178-2220, 2004. (Russian version)

Hildebrand R. On the Number of Independent Control Sequences in the Symmetric Fuller Problem with Two-Dimensional Control. Journal of Mathematical Sciences, 121(2):2221-2225, 2004 (Russian version).

Hildebrand R., Gevers M. Quantification of the variance of estimated transfer functions in the presence of undermodeling. IEEE Transactions on Automatic Control, 49(8):1345-1350, 2004.

Hildebrand R., Lecchini A., Solari G., Gevers M. Prefiltering in Iterative Feedback Tuning: optimization of the prefilter for accuracy. IEEE Transactions on Automatic Control, 49(10):1801-1805, 2004.

Hildebrand R., Lecchini A., Solari G., Gevers M. Asymptotic Accuracy of Iterative Feedback Tuning. IEEE Transactions on Automatic Control, 50(8):1182-1185, 2005.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimal Prefiltering in Iterative Feedback Tuning. IEEE Transactions on Automatic Control, 50(8):1196-1200, 2005.

Bombois X., Scorletti G., Gevers M., Hildebrand R., Van Den Hof P. Least costly identification experiment for control. Automatica, 42(10):1651-1662, 2006.

Hildebrand R. On the approximation of convex functions with cumulant generating functions. Comptes Rendus Acad. Sci. Paris, Ser. I Mathematique, 343(8):545-550, 2006 (link).

Hildebrand R., Solari G. Identification for control: optimal input intended to identify a minimum variance controller. Automatica, 43(5):758-763, 2007.

Hildebrand R. Entangled states close to the maximally mixed state. Physical Review A, 75 (062330) 2007.

Hildebrand R. Exactness of sums of squares relaxations involving 3x3 matrices and Lorentz cones. Linear Algebra and its Applications, 426(3):815-840, 2007.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps. Linear and Multilinear Algebra, 55(6):551-573, 2007 (preprint).

Hildebrand R. Positive maps of second-order cones. Linear and Multilinear Algebra, 55(6):575-597, 2007.

Hildebrand R. Concurrence revisited. Journal of Mathematical Physics, 48 (102108) 2007.

Hildebrand R. Positive partial transpose from spectra. Physical Review A, 76 (052325) 2007.

Poncet P., Hildebrand R., Cottet G.-H., Koumoutsakos P. Spatially distributed control for optimal drag reduction in cylinder wakes. Journal of Fluid Mechanics, 599:111-120, 2008.

Hildebrand R., Mancini S., Severini S. Combinatorial Laplacians and Positivity Under Partial Transpose. Mathematical Structures in Computer Science, 18:205-219, 2008.

Hildebrand R. Semidefinite descriptions of low-dimensional separable matrix cones. Linear Algebra and its Applications, 429(4):901-932, 2008.

Gevers M., Bombois X., Hildebrand R., Solari G. Optimal Experiment Design for Open and Closed-loop System Identification. Communications in Information and Systems, 11(3):197-224, 2011.

Hildebrand R. An LMI description for the cone of Lorentz-positive maps II. Linear and Multilinear Algebra, 59(7):719-731, 2011 (preprint).

Hildebrand R. Barriers on projective convex sets. Discrete and continuous dynamical systems, special issue, pp. 672-683, 2011. (pdf)

Hildebrand R. Half-dimensional immersions in para-Kähler manifolds. International Electronic Journal of Geometry, 4(2):85-113, 2011 (pdf).

Hildebrand R. The cross-ratio manifold: a model of centro-affine geometry. International Electronic Journal of Geometry, 4(2):32-62, 2011 (pdf).

Hildebrand R. The extreme rays of the 5 x 5 copositive cone. Linear Algebra and its Applications, 437(7):1538-1547, 2012. (pdf preprint)

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Geometry of neighbourhoods of singular extremals in problems with multi-dimensional control. Proceedings of the Steklov Institute of Mathematics, 277:74-90, 2012 (in Russian).

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems. Russian Journal Math. Phys., 20(1):25-32, 2013.

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Stochastic dynamics of Lie algebras of Poisson brackets in neighborhoods of nonsmoothness points of Hamiltonians. Doklady Mathematics, 87(3):259-263, 2013.

Dickinson P.J.C., Dür M., Gijben L., Hildebrand R. Irreducible elements of the copositive cone. Linear Algebra and its Applications, 439:1605-1626, 2013. (pdf preprint)

Hildebrand R. On the infinity-norm of the cubic form of complete hyperbolic affine hyperspheres. Results in Mathematics, 64(1):113-119, 2013.

Hildebrand R. A lower bound on the barrier parameter of barriers for convex cones. Mathematical Programming Series A, 142(1):311-329, 2013. (pdf preprint)

Dickinson P.J.C., Dür M., Gijben L., Hildebrand R. Scaling relationship between the copositive cone and Parrilo's first level approximation. Optimization Letters, 7(8):1669-1679, 2013.

Hildebrand R. Hessian potentials with parallel derivatives. Results in Mathematics, 65(3-4):399-413, 2014.

Hildebrand R. Minimal zeros of copositive matrices. Linear Algebra and its Applications, 459:154-174, 2014. (preprint)

Hildebrand R. Canonical barriers on convex cones. Mathematics of Operations Research, 39(3):841-850, 2014. (pdf preprint)

Hildebrand R. Analytic formulas for complete hyperbolic affine spheres. Contributions to Algebra and Geometry, 55(2):497-520, 2014. (preprint)

Hildebrand R., Gevers M., Solari G. Closed-loop Optimal Experiment Design: Solution via Moment Extension. IEEE Transactions on Automatic Control, 60(7):1731-1744, 2015.

Hildebrand R. Centro-affine hypersurface immersions with parallel cubic form. Contributions to Algebra and Geometry, 56(2):593-640, 2015. (preprint)

Zelikin M.I., Lokutsievskiy L.V., Hildebrand R. Typicalness of chaotic fractal behaviour of integral vortices in Hamiltonian systems with discontinuous right hand side. Contemporary Mathematics. Fundamental Directions, 56:5-128, 2015 (in Russian).

Hildebrand R. Spectrahedral cones generated by rank 1 matrices. Journal of Global Optimization, 64(2):349-397, 2016. (pdf preprint)

Dickinson P.J.C., Hildebrand R. Considering copositivity locally. Journal of Mathematical Analysis and Applications, 437(2):1184-1195, 2016. (pdf preprint)

Hildebrand R. Copositive matrices with circulant zero support set. Linear Algebra and its Applications, 514:1-46, 2017. (pdf preprint)

Hildebrand R. Extremal copositive matrices with zero supports of cardinality n-2. Electronic Journal of Linear Algebra, 34:28-34, 2018. (open access)

Hildebrand R. Extremal copositive matrices with minimal zero supports of cardinality two. Linear and Multilinear Algebra, 66(11):2151-2155, 2018. (pdf preprint)

Belomestny D., Hildebrand R., Schoenmakers J. Optimal stopping via pathwise dual empirical maximisation. Applied Mathematics and Optimization, 79(3):715-741, 2019. (pdf preprint)

Hildebrand R. Natural parametrizations of closed projective plane curves. Journal of Geometry, 111(1):17, 2020. (preprint)

Hildebrand R. On the algebraic structure of the copositive cone. Optimization Letters, 14(8):2007-2019, 2020. (preprint)

Hildebrand R. Graph immersions with parallel cubic form. Differential Geometry and its Applications, 74 (101700) 2021. (preprint, link)

Afonin A., Hildebrand R., Dickinson P.J.C. The extreme rays of the 6x6 copositive cone. Journal of Global Optimization, 79(1):153-190, 2021. (preprint)

Hildebrand R. Optimal inequalities between distances in convex projective domains. Journal of Geometric Analysis, 31(11):11357-11385, 2021. (preprint, link)

Hildebrand R. Optimal step length for the Newton method: case of self-concordant functions. Mathematical Methods of Operations Research, 94:253-279, 2021. (preprint, view only version)

Hildebrand R. Self-associated three-dimensional cones. Beiträge zur Algebra und Geometrie, 63:867-906, 2022. (preprint, view only version)

Hildebrand R. Projectively self-concordant barriers. Mathematics of Operations Research, 47(3):2444-2463, 2022. (preprint, link)

Hildebrand R., Ivanova A. Extremal cubics on the circle and the 2-sphere. Results in Mathematics, 77:135, 2022. (preprint,link)

Hildebrand R. Semi-definite representations for sets of cubics on the 2-sphere. Journal of Optimization Theory and Applications, 195:666-675, 2022. (preprint, view only version)

Hildebrand R., Afonin A. On the structure of the 6 x 6 copositive cone. Published online in Linear Algebra and its Applications, 2023. (preprint,link)

Ivanova A.S., Hildebrand R. Optimal step length for the maximal decrease of a self-concordant function by the Newton method. Published online in Optimization Letters, 2023. (preprint,link)


Invited talks

Hildebrand R. Linear group representations in the service of conic optimization. Plenary lecture at 17th International Linear Algebra Society Conference, Braunschweig, Germany, August 2011. (slides)

Hildebrand R. Lower bounds on the barrier parameter of convex cones. Invited talk at 12th International Workshop on High Performance Optimization: Algorithmic convexity and applications, TU Delft, Netherlands, June 2012. (slides)

Hildebrand R., Dickinson P.J.C., Dür M., Gijben L. On the structure of the 5x5 copositive cone. Invited talk at Haifa Matrix Theory Conference, Technion, Haifa, November 2012. (slides)

Hildebrand R. Geometric Aspects of Barriers for 3-Dimensional Cones. Invited talk at Optimization and Applications in Control and Data Science on the occasion of Boris Polyak's 80th birthday. Higher School of Economics, Moscow, May 2015. (slides,video)

Hildebrand R. Scaling points and reach for non-self-scaled barriers. Invited talk at Grenoble Optimization Days 2018, Grenoble, France, June 2018. (slides)

Hildebrand R. Geometry of self-concordant barriers. Mini-course at Summer School Control, Information, Optimization, Voronovo, Russia, June 2019. (link)

Hildebrand R. Minimization of sums of squares of holomorphic functions. Invited talk at Optimization without Borders conference dedicated to the 65th anniversary of Prof. Yurii Nesterov and the 50th anniversary of Prof. Vladimir Protasov, Sochi-Sirius, Russia, July 2021. (link to slides)

Hildebrand R. Numerical range of tuples of matrices and dimensional arguments in proofs in convex optimization. Invited talk at Control, Information, Optimization Summer School dedicated to the memory of Prof. B.T. Polyak, Nizhni Novgorod, Russia, July 2023. (link to summer school website)


Conference proceedings

Hildebrand R., Gevers M. Quantification of the variance of estimated transfer functions in the presence of undermodeling. Proceedings of the 13th IFAC Symposium on System Identification, pp. 1850-1855, Rotterdam, The Netherlands, August 2003.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimal Prefiltering in Iterative Feedback Tuning. Proceedings of the 13th IFAC Symposium on System Identification, pp. 513-518, Rotterdam, The Netherlands, August 2003.

Hildebrand R., Gevers M. Minimizing the worst-case v-gap by optimal input design. Proceedings of the 13th IFAC Symposium on System Identification, pp. 665-670, Rotterdam, The Netherlands, August 2003.

Hildebrand R., Lecchini A., Solari G., Gevers M. Optimization of the prefilter in iterative feedback tuning for improved accuracy of the controller parameter update. Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 4422-4427, Hawaii, USA, December 2003.

Hildebrand R., Gevers M. Identification for control: optimal input design with respect to a worst-case v-gap cost function. Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 996-1001, Hawaii, USA, December 2003.

Bombois X., Scorletti G., Van den Hof P., Gevers M., Hildebrand R. Least costly identification experiment for control. Proc. 16th International Symposium on Mathematical Theory of Networks and Systems, p. 274, Leuven, Belgium, July 2004.

Bombois X., Scorletti G., Gevers M., Hildebrand R., Van den Hof P. Cheapest open-loop identification for control. Proc. of the 43rd IEEE Conference on Decision and Control, pp. 382-387, Atlantis, Bahamas, December 2004.

Hildebrand R. Self-similar trajectories in multi-input systems. Transgressive Computing 2006, A conference in honor of Jean Della-Dora, pp. 287-302, University of Granada, Granada, Spain, April 2006. (pdf)

Hildebrand R. A control problem with a Smale's Horseshoe in the solution. International Conference "Differential Equations and Topology" Dedicated to the Centennial Anniversary of Lev Semenovich Pontryagin, pp. 253-254, Moscow State University, Moscow, Russia, June 2008.

Hildebrand R. Optimal inputs for FIR system identification. Proc. of the 47th IEEE Conference on Decision and Control, pp. 5525-5530, Cancun, Mexico, December 2008.

Hildebrand R., Solari G. Closed-loop Optimal Input Design: the Partial Correlation Approach. Proceedings of the 15th IFAC Symposium on System Identification, pp. 928-933, St. Malo, France, July 2009.

Rojas C.R., Hjalmarsson H., Hildebrand R. MIMO experiment design based on asymptotic model order theory. Proc. of the 48th IEEE Conference on Decision and Control, pp. 488-493, Shanghai, China, December 2009.

Hildebrand R., Gevers M., Solari G. Closed-loop optimal experiment design: The partial correlation approach. Proc. of the 49th IEEE Conference on Decision and Control, pp. 2855-2862, Atlanta, USA, December 2010.

Rojas C.R., Katselis D., Hjalmarsson H., Hildebrand R., Bengtsson M. Chance constrained input design. Proc. of the 50th IEEE Decision and Control and European Control Conference, pp. 2957-2962, Orlando, USA, December 2011.

Despréaux S., Hildebrand R., Maignan A. Graph algorithm for the simulation of the interaction between particles. AIP Conf. Proc. 1479:678-681, International Conference of Numerical Analysis and Applied Mathematics, Kos, Greece, September 2012.

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Generic fractal structure of the optimal synthesis in problems with affine multidimensional control. Proc. European Control Conference 13, pp. 3197-3202, Zürich, Switzerland, July 2013.

Hildebrand R., Gevers M. Central extensions in closed-loop optimal experiment design. Proc. of the 52th IEEE Decision and Control, pp. 5822-5827, Florence, Italy, December 2013. (slides)

Hildebrand R., Lokutsievskiy L.V., Zelikin M.I. Typicalness of chaotic fractal behaviour of integral vortices in Hamiltonian systems with discontinuous right-hand side. International Conference "Optimal Control and Differential Games" dedicated to the 110th Anniversary of L. S. Pontryagin, pp. 124-126, Steklov Mathematical Institute, Moscow, Russia, December 2018.


Other conferences

Hildebrand R. Optimal synthesis of controlled systems near a focus. International Congress of Mathematicians 1998, Abstracts of Short Communications and Poster Sessions, p. 343, Berlin, Germany, August 1998.

Hildebrand R. Classification of optimal syntheses of controlled systems near a focus. Workshop on "Mathematical Control Theory and Robotics", Book of Abstracts, pp. 33-34, SISSA, Trieste, Italy, June 2000.

Hildebrand R. A family of semidefinite relaxations for cones of positive polynomials. Book of Abstracts. 14th Belgian-French-German Conference on Optimization, p. 104, Leuven, Belgium, September 2009. (slides)

Hildebrand R. A Geometric Theory of Barriers in Conic Optimization. SIAM Conference on Optimization 2011 (SIAM OP11), Book of Abstracts, p. 99, Darmstadt, Germany, May 2011. (slides)

Hildebrand R. Semidefinite representations of sets delineated by plane quartics. Book of Abstracts. 15th Austrian-French-German Conference on Optimization, pp. 80-82, Toulouse, France, September 2011. (slides)

Hildebrand R. A barrier on convex cones with parameter equal to the dimension. International Symposium on Mathematical Programming 2012, Book of Abstracts, p. 213, Berlin, Germany, August 2012. (slides)

Gijben L., Dickinson P.J.C., Dür M., Hildebrand R. Scaling relationship between the copositive cone and Parrilo's first level approximation. International Symposium on Mathematical Programming 2012, Book of Abstracts, p. 200, Berlin, Germany, August 2012.

Ninin J., Hildebrand R. Abstract cones of positive polynomials and sums of squares. International Symposium on Mathematical Programming 2012, Book of Abstracts, p. 253, Berlin, Germany, August 2012.

Hildebrand R. Convex projective programming. International Conference on Continuous Optimization (ICCOPT 2013), Book of Abstracts, p. 80, Lisbon, Portugal, July 2013. (slides)

Gijben L., Dickinson P.J.C., Dür M., Hildebrand R. Scaling relationships between the copositive cone and the cone of sums of squares polynomials. International Conference on Continuous Optimization (ICCOPT 2013), Book of Abstracts, p. 66, Lisbon, Portugal, July 2013.

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. 18th European Conference on Mathematics for Industry (ECMI 2014), Book of Abstracts, pp. 337-338, Taormina, Italy, June 2014.

Cottet G.-H., Hildebrand R., Koumoutsakos P., Mimeau C., Mortazavi I., Poncet P. Passive and active flow control using vortex methods. 6th International Conf. on Vortex Flows and Vortex Models, (invited lecture by G.-H. Cottet), Nagoya, Japan, November 2014.

Hildebrand R. Periodic discrete dynamical systems and copositive matrices with circulant zero patterns. SIGOPT 2016 conference. Book of Abstracts, p. 15, Trier, Germany, April 2016. (slides)

Hildebrand R. Barriers on symmetric cones. CORE@50 Bridging Gaps conference. Book of Abstracts, pp. 31-32, Louvain-la-Neuve, Belgium, May 2016. (slides)

Hildebrand R. Barriers on symmetric cones. ICCOPT 2016 conference. Book of Abstracts, p. 75, Tokyo, Japan, August 2016. (slides)

Hildebrand R. Parallelism conditions and algebras in affine differential geometry. PADGE 2017 conference. Book of abstracts, p. 10, Leuven, Belgium, August 2017. (slides)

Hildebrand R. Extremal copositive matrices with zero supports of cardinality n-2. SIGOPT 2018 conference. Book of abstracts, p. 22, Irsee, Germany, March 2018. (slides)

Hildebrand R. Scaling points and reach for non-self-scaled barriers. International Symposium on Mathematical Programming 2018, Book of Abstracts, p. 364, Bordeaux, France, July 2018. (slides)

Hildebrand R. Self-associated three-dimensional cones. Differential Geometry in honor of Udo Simon's 80th birthday, Book of Abstracts, p. 16, Będlewo, Poland, September 2018. (slides)

Hildebrand R. Towards optimal barriers for convex cones. International Conference on Continuous Optimization (ICCOPT 2019), Book of Abstracts, p. 133, Berlin, Germany, August 2019. (slides)

Hildebrand R. On the algebraic structure of the copositive cone. 24th Conference of the International Linear Algebra Society (ILAS 2022), Book of Abstracts, p. 51, Galway, Ireland, June 2022. (slides,abstract)


Conferences for a wider audience

Henrion R., Hildebrand R. Optimization in different flavors. WIASday, Berlin, Germany, February 2015.

Hildebrand R. Introduction en optimisation convexe. Conférence Autour des Mathématiques, 80 ans du CNRS, Bourget-du-Lac, France, May 2019. (slides)


Workshops and external seminars

Hildebrand R. Exactness of the PPT condition for 3x3 matrices and approximation of convex functions with cumulant generating functions. Conference on Positive polynomials, CIRM, Luminy, France, March 2005. (abstract1,abstract2)

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. 14th ERNSI workshop, INMA, UCL, Louvain-la-Neuve, Belgium, September 2005.

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. Convex optimization and applications in control theory, probability and statistics, CIRM, Luminy, France, April 2007. (slides)

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. Differential geometry, Będlewo, Poland, June 2012. (slides)

Hildebrand R. A partial differential equation characterizing determinants of symmetric cones. Mathematics, Algorithms, and Proofs 2012, Konstanz, Germany, September 2012. (slides)

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. Oberwolfach workshop 1415, April 2014. (abstract)

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. Frontiers of High Dimensional Statistics, Optimization, and Econometrics. Moscow, February 2015. (slides,video)

Hildebrand R. Extreme copositive matrices and periodic dynamical systems. Optimization without borders, Dedicated to Yuri Nesterovs 60th birthday. Les Houches, France, February 2016. (slides)

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. Oberwolfach workshop 1744b, October 2017. (slides)

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. Geometry of 3-dimensional cones with applications to optimization. Seminar Optimal Control and Dynamical Systems, Steklov Institute, Russia, November 2022. (slides)

Hildebrand R. On the geometry of 3-dimensional convex cones. Seminar Institut Fourier, Grenoble, November 2022. (slides)


Submitted

Ageron R., Hildebrand R. Improving the constant in Nemirovskis 4/pi theorem. Submitted to Open Journal of Mathematical Optimization, 2021.

Bakhurin S., Hildebrand R., Alkousa M., Titov A. Optimization in complex spaces with the Mixed Newton Method. Submitted to Journal of Global Optimization, 2022. (preprint)

Manainen M., Seliugin M., Tarasov R., Hildebrand R. Generating extreme copositive matrices near matrices obtained from COP-irreducible graphs. Submitted to Linear Algebra and its Applications, 2022.


Preprints and technical notes

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.

Vorontsova E., Hildebrand R., Gasnikov A., Stonyakin F. Convex Optimization. Preprint arXiv 2106.01946 [math.OC], 2021.

Ivanova A., Hildebrand R. Extremal cubics on the circle and the 2-sphere. Preprint arXiv 2110.07946 [math.OC], 2021.

Ivanova A., Hildebrand R. Optimal step length for the maximal decrease of a self-concordant function by the Newton method. Preprint arXiv 2202.06909 [math.OC], 2022.

Bakhurin S., Hildebrand R., Alkousa M., Titov A. Optimization in complex spaces with the Mixed Newton Method. Preprint arXiv 2207.04265 [math.OC], 2022.

Hildebrand R., Afonin A. On the structure of the 6 x 6 copositive cone. Preprint arXiv 2209.08039 [math.OC], 2022.

Last modification: August 24, 2023