On 7 December 2010, Professor Potra celebrated his 60th birthday. To mark this event and to recognize his very many contributions in the field of optimization and in other areas of applied mathematics, we prepared this special issue of Optimization Methods & Software which contains 17 papersFootnote† written by authors who are well-known experts in their areas of research. The topics covered in this volume have either directly or indirectly been influenced by Florian's work and his very many contributions to the field of optimization and applied mathematics in general.
In his 60 years, Professor Potra has had a remarkable journey from his native Romania to his current multiple positions as Professor at the University of Maryland, Baltimore County and Faculty Appointee at the Mathematical and Computational Sciences Division, The National Institute of Standards and Technology.
Florian was born on 7 December 1950 in Cluj, Romania where he finished his undergraduate and graduate (M.S.) studies in mathematics with distinction at the Babes-Bolyai University, one of the best universities in Romania. He continued his Ph.D. at the University of Bucharest under the direction of world-renowned functional analysts, Professors Ciprian Foias and Constantin Apostol graduating in 1980. Soon afterwards in 1982 he received the Andrew Mellon Postdoctoral Fellowship at the University of Pittsburgh where he spent the next two years working with the well-known numerical analyst Professor Werner Rheinboldt. He then assumed a position in the Department of Mathematics at the University of Iowa where he worked until 1997, teaching, mentoring graduate students, doing research and working on many collaborative projects. We were fortunate to meet him there, have him as our teacher and later as our Ph.D. adviser. For his achievements in interdisciplinary research, he received the prestigious James Van Allen Award in Natural Sciences in 1991. After leaving the University of Iowa in 1997, Florian spent a year as the Program Director for Applied and Computational Mathematics at the National Science Foundation. In 1998, he assumed a position in the Department of Mathematics and Statistics at the University of Maryland, Baltimore County and has been there ever since. In 2003, he also joined Mathematical and Computational Sciences Division, at the National Institute of Standards and Technology as an affiliate faculty.
Although he started his career in theoretical mathematics, his diverse interests quickly led him to turn his attention to applied mathematics, especially numerical analysis. His primary focus was the analysis of various aspects and modifications of Newton's method. Florian's transfer to the University of Iowa coincides with the start of the ‘interior-point revolution’, a newly emerging area that revolutionized the field of optimization. At that time the University of Iowa had one of the strongest groups in the world working on interior-point methods. Having already done notable research on various aspects of Newton's method, it is no surprise that he got interested in this emerging field of optimization. Over the years, he authored or co-authored numerous papers making significant contributions to the design and analysis of interior-point methods for various optimization problems including linear optimization, linear and nonlinear complementarity problems and semidefinite optimization problems. It is hard to extract the most significant contribution; however, one that certainly stands out is the design and analysis of the novel corrector–predictor (higher-order) infeasible long-step interior-point methods for sufficient linear complementarity problems that have the best known iteration complexity, that is, the same complexity as that of short-step methods, effectively closing what Professor James Renegar described as ‘the gap between theory and practice’, referring to the fact that long-step methods behave much better in practice than short-step methods but have worse theoretical complexity. Furthermore, the methods are superlinearly convergent even in the absence of strict complementarity and, for the matrix class, do not depend on parameter κ, making them also practically appealing. These results are significant contributions towards improving theoretical complexity of long-step interior-point methods.
Another area in which Florian has made significant contributions is the analysis of mechanical systems with contact and friction. His research in this area stem from his involvement with the National Driving Simulator project at the University of Iowa. Such systems are traditionally described by systems of mixed algebraic differential equations which are very difficult to solve and in some instances solution may not exist. With one of us (Mihai Anitescu), he proposed a discrete model that has a solution under very general conditions and gives very good approximate solutions for a large class of mechanical systems with contact and friction. This method is known as time-stepping scheme. It involves solving nonmonotone linear complementarity problems so Florian's interest in this class of problems is not surprising. The method is based on Moreau's concept that describes such systems as differential inclusions rather than just systems of mixed algebraic differential equations. Moreover, they were able to prove that solutions of the time-stepping scheme converge to the solution of the differential inclusion. Their approach was a key element in alleviating a hundred-year old difficulty in the area, the Painlevé’s paradox.
However, Florian's research interests are far broader and include but are not limited to using numerical and optimization tools in chemical modelling such as air quality and air pollution models, and chemical kinetics models; multi-hazard structural design of atmospheric models; biological models of protein imaging; modeling of wireless networks, specifically mobile ad hoc networks; and PDE constrained optimization models. Florian is a prolific author and a full extent of his research interests and contributions is evident from his book (with Professor V. Ptak), from over 120 published papers in prestigious professional journals, numerous conference proceedings and technical reports, as well as quite a long list of funded grants he has been or is still involved in. His achievements for interdisciplinary research were further recognized when he was selected to be Royden B. Davis Chair for Interdisciplinary Studies at Georgetown University during 2008–2009 academic year where he developed and taught a new course, Simulation of Socioeconomic Behavior. In 2010, he was invited to deliver a prestigious MAA Carriage House Lecture, ‘Mathematics and Robotics’.
In addition to being a prolific author, it is hard to find a colleague who has travelled more, attended more conferences, visited more universities, given more talks than Florian. He is a true leader and ambassador of our profession. He has a remarkable ability to quickly grasp new concepts in very diverse areas, isolating the core problems and offering novel solutions often combining seemingly unrelated research areas. In addition, he seems to have endless energy and enthusiasm and willingness to collaborate and offer encouragement. On numerous occasions, we witnessed him engaged in discussions, filling paper after paper for hours and often being more enthusiastic than the person who initiated the discussion. The beneficiaries of these qualities are his many students and collaborators and the list is quite long and impressive.
There are no signs of Florian slowing down; on the contrary, he is working on many projects and planning new ones in the future. His passion for work is as strong as ever and we are looking forward to his many new contributions for many years to come. Happy birthday Florian and many happy returns!
Many colleagues contributed in making this volume possible. First and foremost, we are grateful to the authors for contributing excellent papers to this special issue. We also want to thank reviewers for their careful reviews of the submitted papers and their cooperation in meeting tight deadlines. Finally, we want to thank Editor-in-Chief, Professor Oleg Burdakov, for his assistance and help during this project.
Notes
†The paper ‘Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints, by A.F. Izmailov, A.L. Pogosyan and M.V. Solodov also dedicated to Prof. Florian Potra has appeared in Vol. 26, no. 4-5, pp. 847–872.