Email: croyer2(at)
For my CV, see here.
La version française de cette page se trouve ici.


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

Clément W. Royer

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 update (September 2017)

Back again in Madison, after a fruitful three-week stay in Europe. Thanks to the organizers of the ALOP autumn school in optimization for machine learning and data science, held at Trier University in Germany, for presenting me with the best poster award. Thanks also to the program committee of the Optimization 2017 conference (held in Lisbon, Portugal) for giving me the opportunity to organize two sessions, and thanks a lot to the speakers for accepting my invitation. Finally, thanks to Youssef Diouane for hosting me at ISAE-SUPAERO: no matter the school, it is always a great pleasure to be back to the University (and to the city) of Toulouse !

Short bio

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

  • From October 2013 to October 2016, I was a PhD candidate in the APO team at the Institut de Recherche en Informatique de Toulouse (IRIT, UMR 5505), under the joint supervision of Serge Gratton and Luís Nunes Vicente. 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.

  • I obtained my Engineer degree in Computer Science and Applied Mathematics from the French Engineering School INP-ENSEEIHT, as well as my Master Degree in Computer Science.
    For more information, you can have a look at my vitae in a short or extended format.

    Research interests

    My research interests essentially revolve around numerical optimization and its applications. My current work focuses in particular on two aspects of the area: the introduction of randomness within otherwise deterministic optimization schemes and the worst-case complexity of general optimization algorithms. Following the lines of my Ph.D., I also maintain a high interest in derivative-free optimization.


    Submitted preprints

    Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization
         C. W. Royer and S. J. Wright.
         Technical Report arXiv:1706.03131, 2017.
    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 and global rates of trust-region methods based on probabilistic models
         S. Gratton , C. W. Royer, L. N. Vicente and Z. Zhang.
         To appear in IMA Journal of Numerical Analysis, 2017.
    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


    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.
         This code is maintained and was used in this work.

    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.
         This code is maintained and was used for this work.

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    Selected talks

    Complexity of line-search methods for nonconvex optimization Slides
         Optimization 2017, Universidade de Lisboa, 2017, Lisbon, Portugal.
         MOPTA Conference, Lehigh University, 2017, Bethlehem, PA, USA.
         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.