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During the last decade, important advances have been achieved in the mathematical modelling of living systems. Recently by considering the bacterial cell as a self-replicating system, a new computational constraint based modelling method named Resource Balance Analysis (RBA) has been developed in my team. From a mathematical point of view, RBA aims at solving a convex optimization problem. RBA has been biologically validated and led to accurate predictions at genome scale of the resource allocation for a wide range of growth conditions. Beyond bacteria, the RBA approach offers a promising framework for the coupling of the cellular scale to the individual scale. Merging all scales will result in many structured, sparse and large optimization problems that are coupled by bio-physical constraints. This representation is generic and transverse to a large diversity of multi cellular organisms like biofilms, plants and animals. In this context, my research project aims to develop new methods and algorithms to solve large and structured optimization problems. Currently, the main optimization methods for solving large problems are gradient based methods which converge slowly and are not very well parallelized in general. To tackle the curse of the dimension of our problems, challenging aspects cover (i) the adaptation of adequate methods for small problems, namely interior point methods, by exploiting the underlying structure of our large optimization problems (typically, by decomposing them into small sub-problems that can be solved simultaneously in parallel); (ii) the adaptation of gradient based methods to our specific problems; (iii) the combination of the previous two kinds of methods.
I am a researcher working in the area of numerical optimization. I obtained a master degree in applied mathematics for economics and finance from Higher National School of Technology (ENSTA), Paris, in 2011. In the same year, I also earned an engineering degree in applied mathematics and computer science from National School of Electrical Engineering, Electronics, Computer Science, Hydraulics and Telecommunications (ENSEEIHT), Toulouse. In 2014, I received my PhD in applied mathematics and computer science from National Institute of Technology (INP), Toulouse, mentored by Prof. Serge Gratton. Between January 2015 and August 2015, I was a assistant lecturer at Paul Sabatier University, Toulouse. Since September 2015, I have a permanent position as young researcher at INRA, Jouy en Josas. My research interests lie at the intersection of numerical optimization, linear algebra and applied probability. I am interested in developing numerical methods for wide class of optimization problems covering convex and nonconvex optimization problems. Thanks to AgreenSkills fellowship, I am currently for one year at King Abdullah University of Science and Technology in Prof. Peter Richtarik team. During this mobility period, I willfocus my research on randomized and hybrid optimization methods with application to living system.
E. Bergou, Y. Diouane and S. Gratton, 2017, On the use of the energy norm in trust-region and adaptive cubic regularization subproblems. Computational Optimization and Applications Journal, 68(3), 533-554.
E. Bergou, S. Gratton and L. N. Vicente, 2016, Levenberg-Marquardt methods based on probabilistic gradient models and inexact subproblem solution, with application to data assimilation, SIAM Journal on Uncertainties Quantification (SIAM/ASA JUQ), 4(1), 92495.
J. Mandel, E. Bergou, S. Gurol and S. Gratton, 2016, Hybrid Levenberg-Marquardt and weak constraint ensemble Kalman smoother method, Nonlinear Processes in Geophysics Journal, 23, 59-73.
E. Bergou, S. Gratton and J. I. Tshimanga, 2014, The exact condition number of the truncated singular value solution of a linear ill-posed problem, SIAM Journal on Matrix Analysis and Applications (SIMAX), 35(3), 10731085.