Nationality: Colombian POEMA Host Institution: CWI, the Netherlands Background: BSc. Math. Universidad de Los Andes,  MSc. Math Universidad de Los Andes Master thesis: Combinatorial Optimization, Optimal Transport , Master thesis: “Maximum Entropy Distribution in Wasserstein Balls” Research interests: Combinatorial Optimization, Polynomial Optimization, Algorithms

POEMA project: Approximation hierarchies for graph parameters

Supervisors:  Monique Laurent, NWO-I/CWI, Amsterdam, the Netherlands

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Nationality: German POEMA Host Institution: LAAS-CNRS, Toulouse, France Background: I studied inUlm (Germany) and Innsbruck (Austria) and my focus was on functional analysis and dynamical systems Master thesis: Global attractors and quantitative aspects of dynamical systems via the Koopman semigroup. A functional analytic approach to slow invariant manifolds.

Research interests: Interplay between geometric aspects of dynamical systems and the Koopman semigroup, “linearized” formulations of problems from dynamical systems in terms of occupation measures (e.g. optimal control) and how to solve them.

POEMA project: Polynomial Optimization: Some challenges from applications. One possible direction is to explore and develope different optimization methods for solving infinite dimensional linear programming problems in the space of Borel measures. Traditionally, the Lasserre’s moment sum-of-squares hierarchy is utilized, which yields a sequence of finite dimensional semidefinite programs. However, there are also other methods that could be applied to this class of problems such as those approximating the gradient flow in the space of measures. The second research direction pertains to reinforcing the existing infinite-dimensional LP formulations such as their finite-dimensional approximations exhibit faster convergence. One possible direction is the connections to the spectral theory of the Koopman and Perron-Frobenius operators. Another direction is the exploitation of the Pontryagin maximum principle. Finally nonlinear (optimal) control problems for partial differential equations have been investigated but very general convergence results for Lasserre’smoment-sum-of-squares hierarchy are not known yet.

Supervisors: Milan Korda, LAAS-CNRS, Toulouse, France

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Nationality: Mexican POEMA Host Institution: Artelys SA, Paris, France Background: I hold a Bachelor’s degree in mathematics by the University of Guadalajara. Latter on, I obtained a Master’s degree in Computer Science, from the Center for Research in Mathematics (CIMAT) in Guanajuato, Mexico. In my Master’s thesis I worked in optimization with orthogonality constraints. I was interested in the Riemannian approach of optimization over smooth manifolds of matrices. In particular, Riemannian conjugate gradient methods rely on the concept of a vector transport to build the search direction. However, using a change of variable the problem can be transformed into an optimization problem over the Euclidean space, where classical optimization methods can be used. This idea lead to a Transportless Conjugate Gradient for Optimization on Stiefel Manifold, my Master’s thesis.

Research interests:

My interests lie both in real world applications of constrained optimization and in the development of efficient algorithms for mathematical programming. In particular, polynomial optimization demands my attention due to its wide applicability and its good performance in global optimization.

POEMA project:

I am participating in POEMA project ESR 15:  Polynomial Optimization Techniques for Energy Network Operation and Design. The main expected result during this project is developing novel practical algorithms based on polynomial relaxations for solving mixed-integer nonlinear programs arising in power systems optimization. A good example is the Optimal Power Flow (OPF) problem where the application of the moment-sos approach for global optimization has shown that the OPF can be successfully convexified for instances where semidefinite programming methods are known to have failed.

This project consists in enumerate, prototype and compare various resolution methods for a given problem. The implementation of the chosen solutions strongly demands reliability and numerical efficiency in order to integrate these features into the nonlinear optimization solver Artelys Knitro.

At Artelys, I will be working with a dynamic high-level R&D IT team.  However, I will be able to beneficiate of the collaboration with other members of the POEMA network. As planned secondments, this project considers research stays at CNRS (Toulouse, France) working with Professor D. Henrion, and at Tilburg University (Tilburg, The Netherlands) working with Professor E. de Klerk.

Supervisors: Michaël Gabay, Artelys SA, Paris, France

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Nationality: Iranian POEMA Host Institution: Univ. of Birmingham, UK Background: M.Sc. Applied Mathematics – Operations Research and Optimization, School of Mathematics, Statistic and Computer Science, University of Tehran (UT), Tehran, Iran B.Sc. Mathematics and Applications, Faculty of Mathematics, K. N. Toosi University of Technology (KNTU), Tehran, Iran Master’s Project: An SQP Algorithm for Nonconvex, Nonsmooth Constrained Optimization

Research interests: Optimization - Linear Programming - Nonlinear Optimization - Convex Optimization - Nonsmooth Optimization - Sequential Quadratic Programming – Multiobjective Optimization

POEMA project:

ESR 13 - “Algorithms and Software for Structured Semidefinite Optimization” at the School of Mathematics of the University of Birmingham.

The purpose is decomposing SDP problems into problems with many small matrix variables or matrix constraints; then, solving them by general purpose SDP software. In order to do this, we will develop algorithms and software for matrix decomposition.

Secondments:   Friedrich-Alexander University of Erlangen and IBM Research in Dublin.

Supervisors:Michal Kocvara, Univ. of Birmingham, UK

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