Research and publications
Email: croyer2(at)


Clément Royer
Wisconsin Institute for Discovery
330 N Orchard St
Madison, WI 53715

Clément W. Royer

La version française de cette page se trouve ici.

Welcome to my web page. Here you can learn a little about me, my research, and my teaching activities. You can also have a look at my publications, the codes that I have written and the talks that I have given.
Enjoy your visit !

Latest news

July 2018 - Back again in Madison, the beginning of summer was rather busy. I attended (as a speaker) the IMA Conference on Numerical Linear Algebra and Optimization at the University of Birmingham (UK). I then organized a session (and also gave a talk) during the ISMP conference in Bordeaux (France). Finally, I visited Serge Gratton and Youssef Diouane in their own facilities of the university of Toulouse (France). Thanks to the both of them for hosting me, thank you to all participants of my ISMP session, thank you to Youssef and Stefan Wild for inviting me in speaking in their session, and thanks to all people with whom I discussed during the past three weeks!

Alongside these activities, I pursued a collaboration with Elhoucine Bergou, Youssef Diouane and Vyascheslav Kungurstev. You can find the resulting report here.

Short bio

  • Since November 2016, I am a postdoctoral research associate in optimization at the Wisconsin Institute for Discovery, in Madison, Wisconsin (USA). I am fortunate to be supervised by Stephen J. Wright.

  • On November 4, 2016, I was granted a PhD in applied mathematics from the university of Toulouse, delivered by the Université Toulouse III Paul Sabatier. It was prepared at the Institut de Recherche en Informatique de Toulouse, under the joint supervision of Serge Gratton and Luís Nunes Vicente.

  • For more information, you can have a look at my vitae in a short or extended format.

    Research interests and publications

    My research essentially revolves around the field of numerical optimization and its applications, particularly in complex systems and data science.
    My current work aims at developing efficient nonconvex optimization algorithms, with a focus on using randomized linear algebra and establishing complexity guarantees.
    Following the lines of my Ph.D., I also maintain a high interest in derivative-free optimization.


    Submitted preprints

    A stochastic Levenberg-Marquardt method using random models with application to data assimilation
         E. Bergou, Y. Diouane, V. Kungurstev and C. W. Royer.
         Technical report arXiv:1807.02176, 2018.
    A Newton-CG algorithm with complexity guarantees for smooth unconstrained optimization
         C. W. Royer, M. O'Neill and S. J. Wright.
         Technical report arXiv:1803.02924, 2018.
    A decoupled first/second-order steps technique for nonconvex nonlinear unconstrained optimization with improved complexity bounds
         S. Gratton , C. W. Royer and L. N. Vicente.
         Preprint 17-21, Dept. Mathematics, Univ. Coimbra, 2017.
    Direct search based on probabilistic feasible descent for bound and linearly constrained problems
         S. Gratton , C. W. Royer, L. N. Vicente and Z. Zhang.
         Preprint 17-10, Dept. Mathematics, Univ. Coimbra, 2017.

    Articles in refereed journals

    Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization
         C. W. Royer and S. J. Wright.
         SIAM Journal on Optimization, 28(2):1448-1477, 2018.
    Complexity and global rates of trust-region methods based on probabilistic models
         S. Gratton , C. W. Royer, L. N. Vicente and Z. Zhang.
         IMA Journal of Numerical Analysis, 38(3):1579-1597, 2018.
    A second-order globally convergent direct-search method and its worst-case complexity
         S. Gratton , C. W. Royer and L. N. Vicente.
         Optimization , 65(6):1105-1128, 2016.
    Direct search based on probabilistic descent
         S. Gratton , C. W. Royer, L. N. Vicente and Z. Zhang.
         SIAM Journal on Optimization, 25(3):1515-1541, 2015.

    Conference proceedings

    On the injectivity and nonfocal domains of the ellipsoid of revolution
         J.-B. Caillau and C. W. Royer.
         Geometric Control Theory and Sub-Riemannian Geometry, 73-86, Springer, 2014
         Proceedings of the INDAM meeting on Geometric Control and sub-Riemannian geometry, May 2012.

    PhD Thesis

    Derivative-Free Optimization Methods based on Probabilistic and Deterministic Properties: Complexity Analysis and Numerical Relevance.
         C.W. Royer, University of Toulouse, November 2016.
         Defence slides

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    DSPFD: Direct Search based on Probabilistic Feasible Descent Sources
         A direct-search MATLAB code for derivative-free optimization. The current version supports unconstrained, bound constrained and linearly constrained problems. It is based on using randomly generated directions to lower the cost in function evaluations compared to deterministic methods, whithout compromising convergence guarantees.
         This code is maintained and was used in this work. On unconstrained problems, it corresponds to the method presented in this paper.

    DESTRESS: DEcoupled Steps in a Trust-REgionS Strategy Sources
         A trust-region method in MATLAB for smooth, unconstrained optimization problems, endowed with second-order convergence guarantees. It relies on the so-called de-coupling technique, that I introduced in my thesis.
         This code is maintained and was used for this work.

    SOUNDS: Second-Order UNconstrained Direct Search Sources
         Direct-search algorithms in MATLAB for smooth, unconstrained, derivative-free optimization problems. The code encompasses several methods that possess (weak or strong) second-order convergence guarantees.
         This code is maintained: it gathers algorithms SDS and AHDS studied in this paper, as well as the de-coupled direct search methods introduced in my thesis.

    LISA: LIne-Search Algorithms Coming soon
         A MATLAB library of line-search methods including classical as well as recently developed frameworks, with a focus on second-order convergent algorithms.
         A preliminary version of this code is available upon request: it implements in particular the second-order line-search techniques introduced in this accepted paper and this submitted preprint.

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    Selected talks

    Complexity of line-search methods for nonconvex optimization Slides
         INFORMS Optimization Society Conference, 2018, Denver, CO, USA.
         CMO Workshop Beyond Convexity: Emerging Challenges in Data Science, 2017, Oaxaca, Mexico.
         Co-author :Stephen J. Wright.

    Numerical Optimization with Probabilistic Guarantees Poster
         Best poster award, ALOP Autumn School, 2017, Trier University, Germany.

    Probabilistic properties in derivative-free and derivative-based optimization methods Slides
    (Original French version)
         SPOC Seminar, Institut de Mathématiques de Bourgogne, 2017, Dijon, France.

    Direct Search Using Probabilistic Feasible Descent for Bound and Linearly Constrained Problems Slides
         SIAM Conference on Optimization, 2017, Vancouver, BC, Canada.
         Co-authors: S. Gratton, L. N. Vicente and Z. Zhang.

    A complete list of my talks and posters is available in my vitae.

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    ENSEEIHT (2013-2016)

    From 2013 to 2016, I was a teaching assistant in the Computer Science and Applied Mathematics Department (IMA in French) at INP-ENSEEIHT. This activity was supported by the CIMI Excellence Laboratory.
    You can find a list of those activities below. Unless otherwise stated, I was involved in the courses during the three years of my Ph.D.

    INP-ENSEEIHT, 1st year IMA
    Hilbertian Analysis
         Practical in MATLAB based on linear algebra aspects from the course of Hilbertian Analysis.
    Analysis Tutorials (2015-2016)
         Tutorial classes focused on ensembles, studies of functions of one variable and topology.
    Differential Calculus (2013-2015)
         Tutorial sessions related to the associated course, covering aspects of differential calculus in finite and infinite dimension.

    INP-ENSEEIHT, 2nd year IMA
    Krylov Space methods
         MATLAB Project on variants of the GMRES method.
    PDE Discretization techniques
         Practical, finite element implementations in MATLAB.
    Concurrent Systems
         Practical parallel programming using OpenMP.
    Numerical Optimization
         MATLAB Practical and Project on continuous optimization.

    For a detailed account of these activities, please have a look at my vitae.

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    This page was designed by Clothilde Royer, many thanks to her.
    Materials on this page are available under Creative Commons CC BY-NC 4.0 license.