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 news

February, 2018 - I attended the MACSER: Multifaceted Mathematics for Rare, High-Impact Events in Complex Energy and Environment Systems annual meeting, held at Argonne National Laboratory on February 8-9. This project and its predecessor have been supporting my appointment in Madison, and optimization under various forms is one of the main axes of investigation.

October, 2017 - The Institute for Foundations of Data Science at UW-Madison has featured my recent work with S. Wright about nonconvex optimization. You can find the news article here and the associated paper (accepted for publication) there. Check also what happened at the BIRS-CMO Workshop Beyond Convexity: Emerging Challenges in Data Science.

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

    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 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.
         Accepted for publication in SIAM Journal on Optimization.
    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.
    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.

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    Selected talks

    Complexity of line-search methods for nonconvex optimization Slides
         CMO Workshop Beyond Convexity: Emerging Challenges in Data Science, 2017, Oaxaca, Mexico.
         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.