Interviewee:  Kees Roos

Interviewer:  Yanqin Bai

  Interview Date:  February 20, 2006

Picture: from left to right:

Kees Roos, Yanqin Bai, Goran   Lesaja  and  Arkadii Nemirovskii 

Introduction 

Prof. Kees Roos is a scientist  who holds a chair in Optimization at Delft University of Technology. Since 1984, when Karmarkar published his path-breaking paper, he started working on interior-point methods for linear optimization. Together with J.-Ph. Vial he presented the first polynomial-time logarithm barrier method for linear optimization; the method has the best known complexity bound. This is one of the milestone papers in the field of interior-point methods. Later on this method was extended to nonlinear convex  problems, including semidefinite optimization and second- order cone optimization problems. Prof. Kees Roos published 140 research papers. He co-authored with J.-Ph. Vial and T.Terlaky the book "Theory and Algorithms for Linear Optimization: An Interior Point Approach, and with Jiming Peng and T.Terlaky the monograph: Self-regularity: A New Paradigm for Primal-Dual Interior Point Methods. His editorial work is for six international journals in the field of optimization. He supervised many PhD students and some of them were awarded by the Dutch Stieltjes Institute. He is the secretary of the Optimization Section of SIAM, the Society Industrial and Applied Mathematics, and he serves as Chair for the Optimization Technology Group in TU Delft.

Next  June a conference is organized to celebrate Prof. C. Roos’ 65th birthday.  (HPOPT 2006 workshop, June 15-16, 2006, Delft, The Netherlands. See http://stuwww.uvt.nl/~edeklerk/hpopt2006/)

1. Your full name, address and e-mail address:

Cornelis Roos,

Mekelweg 4 (Room: HB 07.100)
NL ­ 2628 CD Delft
 P.O. Box 5031 
NL ­ 2600 GA Delft
The Netherlands 

C.Roos@tudelft.nl

2. Your highest degree, awarding institution and year:

Doctoral degree in Mathematics, Delft University of Technology, 1975.

3. How many research papers have you published (including papers accepted   for publication). How many of them in the field of optimization?  

140, 124.

4. Your research interests:

Interior-point methods for convex optimization.

Applications in control theory and combinatorial optimization.

5. Some of your most representative papers or books:

Book:  Theory and Algorithms for Linear Optimization: An Interior Point Approach

6. Please describe your major contributions in optimization: 

In the paper: A polynomial method of approximate centers for the linear rogramming problem, Mathematical Programming, 54: pp295-306, 1992, we showed that the classical logarithmic barrier method, when applied to linear programming yields a polynomial-time algorithm, provided that the parameters in the algorithm are chosen appropriately. We were strongly motivated by Sonnevend’s method of centers and Mediddo’s work on the central trajectory to the optimal set.  

In the paper entitled “A polynomial primal-dual Dikin-type algorithm for linear programming’’, Mathematics of Optimizations Research, 21 (1996),  pp.341-353,  Jansen, Terlaky and I  defined a new primal-dual affine-scaling algorithm and proved its polynomial complexity. This was the first (and only?) polynomial-time affine scaling method.

The last years we created a new paradigm for primal-dual interior-point methods by exploring the fact that almost all known barrier functions depend on simple univariate function, that we called the  kernel function of the barrier function. We could significantly improve the iteration bounds for so-called large-update methods by using new kernel functions. The barrier functions induced by the new kernel functions are not logarithmic.

7. What are the most interesting unsolved problems in the optimization branch you are working on: 

The most challenging problem is for me the so-called “Irony of IPMs “: Small-update methods have the best theoretical iteration bound but large-update methods by far the best performance. The theoretical iteration bound for large-update methods are much worse than those for small-update methods. This gap between theory and practice is very intriguing and has led to the aforementioned kernel-function-based approach. This has decreased the gap considerably, but not yet closed.

Another problem that I would like to work on in the future is the Hirsch conjecture.

Anyhow, I would like to see this conjecture resolved during my lifetime.

8. What kinds of topics excite your research interests?

I am a mathematician, but I prefer to deal with mathematics that can be used to solve real-life problems. That is a major reason why I like the field of Optimization. I have been working in the past on pure mathematics (ring theory), and I liked it very much.

Later on, before 1984, I worked in discrete mathematics, especially algebraic coding theory, and again, I enjoyed it. In that time it happened that I could improve a rather old and well known quality  measure for cyclic codes (the so-called BCH bound); I remember how much excitement  this gave to me (and not only to me). The bound is now known as the ‘Roos’ bound. But precisely in these days, and to the surprise of many colleagues, I moved to the field Optimization. But I never regretted this decision. 

9. How did you develop these interests? What would you say is   one of the most interesting topics you have studied?

I have always been surprised by the ‘power’ of the language of mathematics. It started when I learned Newton’s law. How can it be that many physical phenomena can be described by such a simple formula. It reveals that the reality in which we live is full of structure. The goal of science is to reveal this structure. And it seems that this task is more or less endless. Every discovery raises new questions and gives rise to new research. I find it very hard to think that all this is the result of a chaotic process. On the contrary, it points my thoughts in the direction of God, and the most important to me is that He reveals himself as a God who loves us.

10. To round off the interview, what are some highlights of your career?

It may sound strange, but I was never driven by looking for a career. I was raised in a  rather poor family, without any tradition in science. Most members of my family were fisherman. But they supported me in all possible ways. And so did Leiden University, who offered me a part-time professorship in 1998, and my own university when they appointed me as full professor in 2002. I feel privileged for all the opportunities given to me, and I hope that I can keep serving the community also in the future. I am very honored by the appointment as a guest professor at Shanghai University for the coming years.