Internship Applied Numerical Mathematician

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Objective: investigate nonconvex optimization solving methods that can rapidly converge with few function and derivative evaluations as well as provide and improve second-order information with the same efficiency and reliability as available for first-order information.

Task(s):

Formulate, develop and numerically evaluate enhancements/extensions of computational methods/algorithms including ALM for solving constrained nonconvex optimization problems.

To address the computational performance objectives, the candidate will also actively participate to the design (extension) and evaluation of (existing) automatic differentiation tools for solving such optimization problems.

Integration of these tools into a unified AD framework will be realized in cooperation with computational/numerical method experts. These tasks will be realized under the supervision of a senior (postdoc-level) researcher.

Candidate profile:

MSc (or last year of MSc curriculum) in applied mathematics, mathematical engineering, theoretical computer science, or computer science engineering.

Strong nonlinear modeling and mathematical programming skills.

Very good knowledge of techniques such as first-/second-order iterative methods, inexact methods and Krylov subspace methods ((B)CG, Lanczos, GMRES, MINRES, Arnoldi, etc.) for nonconvex optimization problems.

Experience in programming with nonlinear optimization libraries, e.g., LANCELOT/ CUTE, MINOS, TRON, NLopt, etc.

Excellent written, verbal and interpersonal communication skills.

Knowledge of functional programming language (LISP, Julia, etc.) is considered as a plus.

Objective: instigate and investigate automatic differentiation tools for nonconvex optimization solvers that can rapidly converge with few function and derivative evaluations as well as provide and improve second-order information with the same efficiency and reliability as available for first-order information.

Task(s): design/formulate, develop and numerically evaluate enhancements of existing computational methods/algorithms such as ALM for solving constrained nonconvex optimization problems. To address the computational performance objectives, the candidate will also actively participate to the design (extension) and evaluation of (existing) automatic differentiation tools for solving such optimization problems. These tasks will be realized under the supervision of a senior (postdoc-level) researcher.

Candidate profile:

If MSc thesis: the candidate must be following the last year of the curriculum in, e.g., applied mathematics, Math. Engineering, Theoretical computer science, Computer science engineering. Detailed coordinates of MSc promotor and his/her academic affiliation must be provided in the CV application form.

If internship: the candidate must have completed his/her MSc (in one of these disciplines) and ideally realized a thesis in one of the following domain(s): nonlinear programming, computational methods and algorithms for nonconvex optimization (incl. second order iterative methods, subspace methods, etc.), automatic differentiation. Copy of the MSc diploma/ certificate shall be included in annex of the CV. The internship can also be considered as part of post-MSc graduation or PhD graduation program.

Good knowledge of functional programming language (LISP, Julia, etc.) is considered as a plus.

Objective: automatic labeling method of network data, including spatio-temporal data (traffic, etc.), structural data (topological, etc.)

Task: blends modeling, algorithmic and experimental research; the candidate will have the opportunity to explore, evaluate and compare different labeling algorithms by formal and numerical methods. These tasks will be realized under supervision of senior (postdoc-level) researcher.

Application requirements for all Internships :

Certified copy of the MSc diploma/certificate shall be included in annex of the CV.

The CV shall indicate the detailed coordinates of the current or eventually the last academic institution and department of the candidate.

The CV shall include a detailed list of publications/achievements in relation to the job description.

Note well: the candidate must follow or have obtained his/her MSc degree from an academic institution of one of the EU countries.

Duration:

Short duration (from 3 to 6 months): suited for MSc curriculum course

Long duration (up to 12 months): suited for MSc thesis internship