We welcome Jan Kronqvist, new member of the faculty at the Department of Mathematics

Jan Kronqvist completed his PhD at Åbo Akademi University in Turku, Finland, during which he spent half a year as a visiting researcher at Carnegie Mellon University in Pittsburgh, USA. Subsequently, he did a 2-year postdoc at Imperial College London as a Newton International Research Fellow before moving to Sweden to join the division Optimization and System Theory. His main research interests are in the field of mixed-integer optimization. His research focuses on developing algorithms and computational techniques for solving mixed-integer problems, and mixed-integer optimization techniques for ML and AI.

Welcome to KTH! Tell us a bit about yourself. What inspired your interest in mathematics?

I have always been interested in technology and making things work better. As a teenager, I was actually building jet engines as a hobby. Then I quickly realized that in order to get a deeper understanding and improve things you need a bit more math. You quite quickly run into some differential equations and other topics in order to optimize engines. I would say that this really boosted my interest in applied mathematics. However, I have always had a strong interest in mathematics. My research in mixed-integer optimization covers theoretical and fundamental topics, but also more applied and computational topics. Personally, I enjoy this mixture of both theoretical and applied research. 

What motivated you to move to KTH and Sweden?

KTH has a strong international reputation, and I think it is an excellent environment for my research. At KTH we are several people working on fundamental mathematical aspects of optimization and developing algorithms, and other researchers are focusing on applications where optimization is used as a tool. The combination of more theoretical and more applied research makes KTH a great environment.  

I am born in Finland, but my mother tongue is actually Swedish as I grew up in a Swedish-speaking region of Finland. Compared to the USA or UK, moving to Sweden felt more like moving home. To me, the culture is pretty similar as in the Swedish-speaking parts of Finland. I think people in Sweden are overall very friendly, and I enjoy living here. Stockholm is also a very beautiful city, and I enjoy that it is small enough that you can explore it by foot.  

What is your research about?   

My research focuses on developing techniques and algorithms to solve nonconvex optimization problems, specifically problems where the nonconvexity originates from integer variables. I have specialized in optimization problems with both continuous and integer variables as well as some nonlinear relations. This type of optimization problems is commonly called mixed-integer nonlinear programming (MINLP). The integer variables give great flexibility in modeling processes and systems as they can be used to encode on/off constraints and logic relations. There is a large number of different applications of MINLP optimization, where great benefits can be obtained by finding and implementing optimal solutions. Solving problems of relevant size is still challenging, but great progress has been made.  

If you ask me, it is the integer variables that make it really interesting. The integer restrictions are often the source of the difficulty, but by exploiting certain problem properties we can derive algorithms to solve them efficiently.  

Are you planning to develop your research in new directions?

I am interested in new frameworks for integrating and developing mixed-integer optimization techniques for machine learning (ML) and AI. I believe there could be great benefits of using mixed-integer optimization more in ML and AI, but the challenges related to solving large-scale mixed-integer problems are still a limiting factor. Many of the problems resulting from ML and AI applications are highly structured, and by utilizing these structures, I believe they could be solved efficiently. Learning to deal with such structures in optimization problems would not only benefit the fields of AI and ML, but would also bring benefits to operations research. Therefore, I think there will be various benefits from exploring and developing mixed-integer optimization for AI and ML.  

What do you view as your most important research accomplishment?

I have developed several algorithms for a class of optimization problems called convex MINLP (these are problems that become convex if we relax the integer variables as continuous). By integrating these algorithms together with some other techniques, it was possible to obtain great algorithmic synergies. There were several problems that first took us hours to solve that we are now able to solve in a few seconds with the new techniques. Together with a colleague we developed these techniques into an open-source solver, SHOT , which is currently considered as the most efficient tool for solving these types of optimization problems. With the solver I feel that we pushed the field a clear step forward.  

For the solver we were awarded the COIN-OR Cup in 2018 at INFORMS Annual Meeting in Phoenix, for best contribution to the open-source initiative in operations research and optimization. The research also led to an increased interest in the field of convex MINLP, and a competition between solver developers that has led to further progress.

What were the effects of the pandemic on your work?

For ongoing projects, I have been able to continue my research without any major difficulties as my work focuses on developing theory and running computations. My research mainly requires access to literature, pen and paper, and a computer. I can imagine the pandemic must have been difficult times for more experimental research.

However, I have greatly missed daily interactions with colleagues. In my experience, it is important to be able to talk spontaneously to people to come up with new ideas and collaborations. The opportunities to meet someone while getting a cup of coffee do not happen virtually.  

 During the pandemic, it has been more difficult to start new projects and collaborations. I think the main reason is the more limited interactions with colleagues, both on a day-to-day basis and interactions during conferences and other events.

What is your advice to researchers that are looking for an academic position at this period?

I think one of the challenges during the pandemic has been to get visibility and making other people aware of your research. Especially as a PhD or Postdoc looking for the next step, it is important that other people in the field are aware of you and know of your research. Virtual conferences are ok, but in my experience the audience tends to be smaller.

To gain more visibility, I would advise early-career researchers to also upload your virtual presentations to YouTube. It is a bit of extra work, as you probably want to edit the video before uploading it, but it gives you a much bigger audience.  

What do you enjoy doing in your free time? Have your hobbies changed during the pandemic?

Due to the pandemic, I have started exercising and walking more. In the beginning of the pandemic, I started walking back and forth to my office at Imperial College. I did not really feel comfortable taking the tube during the pandemic. But, on the positive side it gave me the motivation to exercise more.

I think Stockholm is a very beautiful city, and I enjoy walking and exploring the city together with my wife. In the summer, I also enjoy sailing and being out on the water.