PhD position on Constrained Optimization with Low-Rank Tensor Approximations – TENORS DC15

This PhD position is funded by the Marie Skłodowska-Curie program of European Union through the innovative training network (ITN) TENORS.

More information and applications here.

Why join Artelys?

Artelys is an international company based in France (HQ), with offices in Brussels (Belgium), Chicago (US), Milan (Italy) , Madrid (Spain) and Montréal (Canada).  Artelys is specialized in optimization, decision-making and modeling. Relying on their high level of expertise in quantitative methods, Artelys’ consultants deliver efficient solutions to complex business problems. They provide services to numerous industries: Energy & Environment, Logistics & Transportation, Telecommunications, Finance, Defense, etc.

Artelys offers a wide variety of services, including software solutions (optimization solvers, business specific solutions & specific software developments), consulting, project management assistance, training, etc. For instance, Artelys develops Knitro, a state-of-the-art nonlinear optimization solver, and also the Artelys Crystal software suite which addresses specific business problems (especially in the energy sector and planning) including optimization and visualization tools.

The company was founded with an ambition to provide sound quantitative analysis for daily business decisions and its reputation and growth rely on a number of key values such as competence and experience, commitment to deliver and client satisfaction.


In certain applications, the desired solution of an optimization problem can be stated as a tensor. Typically, the size of such a tensor grows exponentially in problem dimension. To deal with this so-called curse of dimensionality, low-rank tensor decompositions have been developed and used to provide compressed approximations to the original tensors. An important application area is the simulation of high-dimensional PDEs, in which case the tensor contains a certain discretization of the solution operator of a PDE (i.e. a multivariate function). Having the solution operator in a tensor is different than having the problem data in a tensor: the desired tensor is given only implicitly, and an algorithm for solving such an optimization problem needs to work with the low-rank representation.

In the first phase of this project, we consider constrained optimization problems with variables in the form of a low-rank tensor decomposition. There are a number of studies in the literature that extend optimization algorithms for tensor variables by using tensor algebra. An alternative approach is to input variables into an existing optimization algorithm directly in the form of its low rank decomposition. The challenges of the approach have been studied in the context of unconstrained tensor optimization problems arising in tensor completion; in this project, we aim at the design, implementation and analysis of new algorithms by extending this approach to constrained optimization. In the second phase, we consider optimization problems with constraints evaluated through tensor-based surrogates (such as machine learning models or simulations). The goal of this phase of the project is to extend existing constrained optimization methods to exploit the special structure of the surrogate models, and possibly deal with the error in resulting constraint evaluations.

Supervisor: Bernard Mourrain, INRIA


  • Figen Öztoprak Topkaya, Artelys, Gebze Technical University (GTU)
  • Michaël Gabay, Artelys
  • Cordian Riener, Arctic University of Norway (UiT)


The main expected result during this thesis is practical algorithms with a theoretical basis for solving constrained optimization problems with variables in the form of low-rank tensor decompositions, and problems involving tensor-based surrogate models. Writing conference/journal papers and completion of a PhD degree by the Doctoral Candidate.


The PhD will be a double degree, awarded jointly by universities of Nice, France and the Arctic University of Norway (UiT). The candidate will spend 10 to 12 months in Norway, at UiT (Norway).


  1. Have — at the date of recruitment — a Master’s degree in Computer Science, Mathematics or Engineering (or any equivalent diploma).
  2. Trans-national mobility: The applicant — at the date of recruitment— should not have resided in the country where the research training takes place for more than 12 months in the 3 years immediately prior to recruitment, and not have carried out their main activity (work, studies, etc.) in that country. For refugees under the Geneva Convention (1951 Refugee Convention and the 1967 Protocol), the refugee procedure (i.e. before refugee status is conferred) will not be counted as ‘period of residence/activity in the country of the beneficiary’.
  3. Be able to communicate fluently in English (speaking and writing). Oral interview with the prospective advisor may be required.

required skills

Ideal candidates must have a master degree in computer science and/or applied mathematics. You should have a solid background in numerical optimization. You are curious and enthusiast to exploit your computer development skills and your knowledge of optimization research.

Operational on various contexts and real issues. Rigorous and passionate, you show initiative and imagination and already have an ease in programming and scientific languages (C/C++, Python, R, Julia).

During this thesis, you will be brought to develop your skills in:

  • Nonlinear optimization
  • Tensor numerical methods
  • Software development and programming
  • Versioning, Integration (Git, Jenkins, Maven)

The candidate should be fluent in English. Knowledge of French is an asset.

procedures for application

  • All candidates must apply via and specify DC15 in the title of their application
  • The applications closing date is March 31, 2024.
  • Interviews will be conducted in Paris and remotely in April 2024
  • The start of this position will be in September 2024 and will last 3 years maximum.


This is your dream job? Apply now!



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