Thursday 23 April 2015

Michael J. D. Powell (1936 - 2015)

Michael James David Powell passed away on April 19th, 2015.

On this memorial site, family, friends, students, and colleagues are invited to leave a message in remembrance and celebration of an inspiring mathematician and founding father of optimization and other branches of numerical analysis.


  1. Mike set the tone for nonlinear optimization research that started in the 1960s. A whole generation followed his vision, where the ultimate goal is the creation of new algorithms and theoretical analysis is a tool for achieving the goal. He devoted years to the understanding of quasi-Newton methods---leading to his beautiful and brilliant analysis of BFGS---but he would often comment with a twinkle in his eyes that the lack of a convergence proof for the non-convex case did not stop anyone from using it in practice.

  2. My fondest memories of Mike are really memories of Mike and Caroline. They were the most solicitous hosts and easy guests. He was truly unique, and it will be strange not to have him with us. The end of an era has come.

  3. It is so strange to contemplate a world without Mike. He has always been there. Right from my pre-student days at NPL where I learned of the "complementary DFP" update, through anecdotal stories of the Harwell-Oxford seminar series in which speakers would wither under Mike's so-incisive questioning, to his support of my career in so many direct and indiect ways. Mike and Roger Fletcher set the standards by which modern nonlinear programming is measured. He was a great believer in rigour, but he also never lost sight that the purpose of analysis is understanding. And he was passionate that his job was not done until he had implemented, tested and distributed his ideas as (often quirkily-named) software.

    Mike, of course, set up the NA Group at AERE Harwell, so without Mike, I wouldn't be where I am now. He established the Harwell Subroutine Library over fifty years ago, and this too is still going strong. He was a devoted attendee at meetings all over the world; I believe that he attended all but one of the Dundee meetings, often with Caroline. Nobody will ever forget his ever-so colourful hand-drawn overheads (Powell-point, as Dominique Orban refers to them) and his deep distrust of some forms of technology. And Mike was an inspiring supervisor of students. His academic children and grand children hold many top university positions.

    I am so grateful that I knew Mike. I miss him.

  4. In 1976 I took half a year off from university to visit DAMTP at Cambridge. I remember everybody saying, Mike Powell is about to arrive! I must have missed him by a few weeks, for he took up his chair that autumn.

    Once I got to know him soon after, he was very good to me and always a landmark of a very special person and scholar. He invited me to Cambridge in the summer of 1985, a wonderful few months for me. At the end of August, on my 30th birthday, was the Fox Prize event at which Mike was the chair and I was the winner (and five years older than the other contestants, I hasten to add). My parents were in town for the occasion and got to know Mike over a celebratory tea afterwards (in those days you couldn't buy a beer in the late afternoon). My mother was very impressed with Mike and considered that I was very fortunate to have such a senior colleague. She was right.

  5. To my supervisor, from his last PhD student: A huge thank you for everything you have done for me. You have taught me how to do research, think critically, ask questions and dare to look for answers. Not to believe but to challenge the status quo (especially numerical results !), before possibly accepting it. Not to follow research fashions but to stay with the good questions whether they are popular or not (provided they are important ones). That theory is a means to an end rather than an end in itself, and that the purpose of it all is to provide useful software for users (this has inspired me though I have not been able to always/fully follow this viewpoint in my research).

    As a person, you have impressed me with your profound sense of duty (at all costs), with your kindness, and your willingness to help in difficult moments of my research and my life.

    I also thank you and Caroline for your very kind hospitality in your home throughout my PhD years and beyond. It has set up a (high and worthy) standard
    for Jared and I in how we try to look after our own students, group members and colleagues. I will never forget and always be grateful.

  6. Modern nonlinear programming began about 1958 with the advent of digital computers. While working in industry in 1963 I was assigned to a project that required computer solution to a nonlinear programming problem. A search of the literature at that time led directly to Mike and to Roger Fletcher. What I really appreciated was that however theoretical their work it always was concerned with an underlying algorithm which had been programmed and tested. I developed a lifelong interest in software for math programming algorithms. When I met Mike, he was very generous in sharing his software with me. i quickly discovered that in order to make the codes as efficient as possible, Mike was an expert at diabolical use of the three way IF statement in FORTRAN II. (In Turing terms, true, false and other). The result of this was codes that required an NSA decryption specialist to interpret. I think if Mike had applied this talent to actual encryption if he could have created a code that would defeat even Turing. At least it would have been a great contest of two Cambridge titans.

  7. Mike invited me to spend the 1978-79 academic year at Cambridge, and I have many fond memories from this time, but also from the times that we got together. During his visits to Argonne, I would try to have a new game to play with Mike; this would give me an edge. But it would not take long for him to get the hang of the game, and for me to loose the edge and the game. It was great fun.

    The impact of his theoretical work on the optimization field is undeniable. My favorite results are his proof of the global convergence of the BFGS method for convex functions, and the introduction of the least change approach for derivative-free optimization. I was present when he presented these results, and was amazed at his mastery of the material; it was sheer beauty and magic. His impact on software development is also remarkable. His codes, although written in a highly unusual style, had superb performance. Many of us labored long and hard, trying to improve on the performance of these codes.

    He shared his ideas freely and never asked for anything in return. He was truly generous. I considered him a friend and mentor. I will miss him.

  8. My admiration towards Mike started about 20 years ago when I attended his seminar in Sydney, Australia and it has grown steadily over the years. Initially, I admired him as the father of optimization and someone who has a brilliant mind. Since moving to Cambridge, I have had the privilege to meet him in person and become closer to him over the last couple of years. It was a humble and fascinating experience to watch him working with teenager friends on tricky Mathematical Olympiad questions in a garden party. We were also lucky to have him and Caroline to celebrate the Tour de France together in the front of our house in July 2014. Mike's kindness and affability made him a wonderful person to be with. Mike, we will miss you dearly.

  9. As David Shanno notes, Mike was diabolically clever with GOTOs, including in one code an assigned GOTO in Fortran that took a couple of us a good while to sort out. It is worth us all looking at our own codes to see how much the tools we used when learning computing shape the structure of the programs we write. I'm still hoping to sort out some of Mike's codes so they can more easily or more effectively installed in other systems (I use R, for example).

    Mike was always generous to me, even though we had different approaches to how optimization software should work. He felt users should know how to set control parameters. I know they won't! But from that difference of view we can hope to find ways to improve the tools to at least avoid users getting "answers" that are silly or even dangerous.

    He will be missed.


  10. Goodbye Prof. Powell. R.I.P

  11. Prof. Powell interacted graciously with my students and me. He patiently answered our questions and offered helpful suggestions. He was a gentleman and a scholar.

  12. As many others have remarked, Mike Powell set a standard for all numerical analysts in terms of mathematical rigour and persistence in unravelling problems while allowing vanishingly small tolerances for loose ends! Hatfield is quite close to Harwell and to Cambridge and, along with colleagues at the Numerical Optimisation Centre, I was able to hear Mike quite often at afternoon seminars. It is hard now to imagine his absence.

    Mike Bartholomew-Biggs

  13. As John Dennis said, this really is (at least partially) the end of an era. I was very fortunate to be a participant near the early stage of that era, when John and I spent 4 months with Mike et al at Harwell in early 1976 while I was a graduate student. Mike had all the wonderful qualities that people have commented on above and it was a dream time as a grad student. Three quick recollections of those days at Harwell: a) the academic debates that went on at the lunch table daily - fortunately grad students were spared from being tested quite as hard as everyone else; b) witnessing Mike write a research paper in longhand on lined paper in one draft with no corrections and hand it to an assistant to type - he was that disciplined and that good; c) giving a short course at Harwell where the speakers were listed as Dr. Dennis, Dr. Reid, Mr. Powell and Mr. Schnabel (Mike was already the leader of the optimization field but had not studied for a PhD). And a final vintage-Mike moment: taking him hiking on a high mountain in Colorado and trying to convince him to turn around on a very exposed open slope in impending bad weather when he was intent on reaching a certain mark on his altimeter. That was harder than quasi-Newton convergence proofs.

    Bobby Schnabel

  14. In 1975 I met Mike at the Dundee conference. Neither then nor since
    have I been working in but rather with optimization. When I started
    a related service around 1996 at
    I asked him for permission to post his codes. He replied:
    "Thank-you for your message. I will be delighted if you will give
    some publicity to COBYLA in your www pages. I really do write software
    for other people to use."
    Since then he has sent me every new program and I have posted it and
    also added links to versions in other languages.
    I met him last at ISMP 2012 and will miss him.

  15. There were two Mike Powells: the gracious host and the congenial guest, the kind and generous companion, the collegial and scholarly scientist but at the same time, when competition was called for, the uncompromising optimiser. In one of my rare visits to Cambridge, Mike kindly invited me to lunch in his college but I was an inconsiderate guest and arrived a little late. This put us out of step with the other diners but the real disappointment was missing out on the game of bowls which followed lunch. All we could do was watch the game from the sidelines. I asked him questions about the rules of the game such as what happens if the bowl hits a tree and how is the score calculated. There turned out to be many possible answers, depending on the specific college where the game is being played. One of the scoring systems was due to G. H. Hardy! It looked as though the feasible region and the objective function were college-dependent and perhaps Mike had an algorithm for each venue. We will all miss Mike as a bright star in the numerical analysis constellation but we will all benefit from his legacy of reliable algorithms and a standard of gentlemanly behaviour.

  16. I only met Mike crossing him in the corridor at his home as Caroline hosted us for a Quaker project... I went to his funeral in support of Caroline, only to find out there who Michael really was! It was particularly touching for me, as my cousin George read maths at Trinity and my nephew Kristof applied at Saint Catharine's to read Applied Maths - their common high school in Budapest sends a reported 9 students per year to Cambridge, and they might know Dr Orban who set this blog up - I met Mike's younger daughter briefly over a minor matter after the service, but the whole family across the aisle looked lovely. Thanks again for bringing so many together in what to me was a celebration.

  17. I was immensely fortunate to do my undergraduate studies at Cambridge, which meant that my first exposure to numerical analysis would be through Mike or Arieh. In my case it was Mike. I took two courses with him, the introductory numerical analysis and his Approximation Methods course. Mike was a simply fantastic teacher. If a student did not understand something then Mike considered that he had failed as a teacher, not that the student had failed. That was the first time I knowingly encountered that outlook on teaching, and it has affected my own teaching philosophy far more than any of the trendy courses on 'learning outcomes' I have occasionally had inflicted on me since. But Mike affected me not only with teaching outlook and methods, but also with the material he taught. I think Approximation theory and methods gave me my first insights into what applied mathematics is and can be, and still affects how I do my numerical analysis to this day. So I never knew Mike as a colleague or a friend, but he was a profound influence, and one I greatly appreciated. He will be missed.

  18. I've enjoyed reading the other tributes to Mike, which are so richly deserved. I wanted to share just one personal memory, about the first time I met Mike. It was at Argonne in 1990, during one of the visits that Jorge More' mentioned. I was quite nervous about meeting the famous man, whose work I had revered since taking my first optimization class in the early 80s. Mike came to my office and asked me to describe my current interests, so I started to tell him about the interior-point papers I'd been reading. I hadn't really started to work in the area myself, but I told him (still nervously) about one of the lines of research that I was thinking of pursuing. Mike responded "yes... yes..." and then: "In my opinion, that's completely the wrong approach!" At this, I forgot about being nervous, jumped up from my chair, and went to the blackboard to defend myself vigorously. Mike listened carefully, then agreed: "There might be something there." Mike brought me out of my shell by treating me as a colleague, though
    I was very green in those days. In my whole career, it is probably the research discussion that I remember most vividly.

    During that discussion, Mike wrote a formula near the top of my blackboard. I drew a line around it and preserved it as my memento of Mike's visit. It stayed until the blackboards were replaced by whiteboards, eight or nine years later.

  19. I am not very gifted at writing something at such sad occasions. I knew Mike for so many years. He and Caroline were friends. Without him, our community will not be the same. We will all miss him.

  20. Mike was an outstanding ambassador for optimization, approximation theory, and numerical analysis in general, combining an uncompromisingly rigorous approach to science with a true concern for colleagues and especially younger researchers. I remember hikes and wine at many conferences around the world: a wonderful hike with Martin Buhmann and Pete Stewart before one of the Dundee conferences, where I was glad that Pete could join me in pleading for a brief rest,
    and a pleasant hike in a gorge near Cornell where Mike insisted on climbing over a barrier to reach the top of the second-highest waterfall in the US east of the Rockies.

    On that same trip, Mike bought a bottle of hybrid NY wine rather than the better vinifera varieties, because he wanted to get a taste of the local (vini)culture.
    That evening, I was pleased to beat Mike at table tennis, not an easy task because of his very competitive spirit, but I had local knowledge in my favour though I was a little scared at causing brain damage to the leading nonlinear optimizer from too frequent contact with a large overhead pipe.

    Mike and Caroline were great hosts when I spent a sabbatical at DAMTP, where I had the privilege of watching Mike load his deck of Fortran cards while the rest of us used monitors. Mike also arranged for me to give talks around the UK and participate in a summer school the next summer in Lancaster.

    Wherever I met Mike, in Oberwolfach, ISMP meetings, or Mexico, often with Caroline, he was a central figure, making new contacts and catching up with old friends. He criticized overly chilled white wines at receptions in every continent, and graciously bought me a bottle of German wine at Oberwolfach after my somewhat garbled description of how I thought I had solved a problem he posed about convergence to as global minimum. Maybe we were drinking that when he and Roger Fletcher introduced me to bridge misere, which I never quite got.

    Mike gave fascinating talks with inimitable style. He was one of the few researchers I have known whose voice made itself apparent as you read his papers. I still remember one where his dry humour emerged after ten pages when I realized that what I thought was a capital "em" was actually a capital "mu".

    I last saw Mike at the SIAM Optimization meeting in San Diego, where it was great to catch up with him over a cold glass of California chardonnay. Mike was a wonderful role model for so many, and will be greatly missed.

  21. Including two photos of typical Mike's presentation, this one in Birmingham, September 2012. I will miss him.

  22. This has been the cause of great sadness for my family & myself. An old oak tree has just fallen, what a giant and what deep roots have been left behind.

    [With apologies but also credit to Mike Todd who is liberally misquoted below.] The first time I remember hearing Mike talk was a seminar to explain that Karmarkar’s worst case complexity bound for linear programs was actually tight. This was 1991 or 92, probably in the ORIE Dept at Cornell, and Mike Todd gave the introduction. He said, Powell is the “P” in DFP and most of us think of him as the “P” in NLP. That was absolutely perfect. In fact Mike P was a giant before I even had nappies: his DFP paper, with Roger Fletcher, was published the year I was born!

    I only really met Mike properly when I moved to Cambridge - knowing he was here was a great attraction. He was formidable both physically and mentally but always keen to discuss ideas and in no way condescending. Also great company with Caroline over dinner! In the last decade or so it’s been inspiring to see him leading development of a new generation of methods for optimization problems, still based on quadratic models, as DFP is, but entirely without derivatives. Mike's ideas and his algorithms will iterate on!

  23. I have many strong and happy memories of Mike Powell.

    I first recollect meeting Mike on a one-to-one basis when I was
    a graduate student in Oxford when he was leading the Numerical
    Analysis Group at AERE Harwell then situated in the Theoretical
    Physics Division. One of my enduring memories was being very
    impressed at coffee time when he with Mike Hebden and Roger
    Fletcher replayed their bridge games of the previous night by memory,
    analysing every play in the game and discussing whether they had reached the
    optimal contract. This intensity continued at lunch when discussing
    work and was an amazing if intimidating training for a young researcher.
    In fact, throughout my career, I always had just that slight apprehension
    when talking to Mike as he was so perceptive with an amazing ability to
    find the crux of any mathematically expressed problem even in areas where
    he was not doing his own research. However, although apprehensive I very
    much appreciated and even enjoyed such exchanges as Mike was really
    trying to help one to a greater understanding and indeed did so
    on many occasions. In his own area, Mike was unbelievably brilliant.
    He could conjure counter-examples with amazing precision and speed and had
    an outstanding ability to choose the many fudge parameters that keep
    appearing in optimization. His coding style was quite unique and
    the story was that he developed it in the days of punched cards so that,
    if the deck was dropped, it had a remarkable resistance to a small amount
    of card shuffling.

    Mike had a very major influence on my life. After I had spent time in
    the USA and lecturing in Newcastle upon Tyne, he persuaded me to leave
    academic life for Harwell where a permanent post was available following
    the departure of Roger Fletcher for Dundee. The irony of Mike leaving
    Harwell for Cambridge the year after I arrived was not lost on either
    of us but I must say that I have not regretted succumbing to Mike's
    persuasive powers, aided by excellent meals from Caroline.

    Mike's intensely competitive approach to research was completely mirrored
    in his attitude to sport. He welcomed me to the Harwell hockey club
    where he was for some time captain of the second eleven, and I copied
    or tried to copy his style in mid-defence so that few people got past
    me without regretting doing so. The only sport at which I was able to
    win against Mike was at squash but sometimes that was a terrifying experience
    as he expanded his large frame to encompass most of the court including
    where I was standing. On one of my visits to Cambridge, wonderfully
    hosted by the Powell family with intellectual rigour in the evenings
    from their copious board games cupboard, I had the ambiguous pleasure
    of playing Pembroke bowls which bore only a passing resemblance to the
    lawn green bowling which I was playing regularly at the time.

    It is really difficult to believe that Mike has left us and we cannot
    enjoy his energy, enthusiasm, and love for mathematics and life but
    he has left us with an enduring legacy of major contributions to
    many areas of numerical mathematics and an abundance of cherished memories.

  24. I had contact with Mike Powell since 1995 when I was writing PROC NLP for SAS Institute in Cary NC. It was the same year when I started writing my matrix language CMAT. And I was swept away by Mike's response when he mailed me all of his Fortran subroutines which had been included into the Harwell library. He encouraged me to include most of his code into my CMAT program and put me in his mailing list. From then on I always was up-to-date whenever he had finished another algorithm for numerical optimization. Very, very rarely he reported some little bug, and moved on to write even more of his very fast and reliable algorithms. When he went last year to the Amazonas and later to Hongkong, he sounded so healthy that I was completely shocked when I read about his dead in the SIAM Newsletter SIAG OPT Views and News. I feel very, very sorry about this bad News and wish his wife all the best to recover from her loss.

    Wolfgang Hartmann
    from 1986 until 2007 SAS Institute, Cary NC
    now retired Mathematician in Heidelberg

  25. I had the pleasure of playing with Mike at our Spring Golf meeting played at Brancaster in 2009. Mike was a great competitor and superb fun to be around and whilst my knowledge of the Mathematical world he immersed himself in was somewhat limited (non-existent) we had a superb round and fun lunch afterwards. Condolences to his wife, family and friends at this time.

  26. Professor Powell was my academic grandfather --- I did my Ph.D. under the supervision of Professor Ya-xiang Yuan. I met Professor Powell only a few times, but we had many email exchanges, because my Ph.D. thesis was on optimization methods without using derivative (aka, derivative-free optimization, DFO), a topic that Professor Powell worked on since the 1960s until the final days of his life.

    Professor Powell was exceptionally kind to me. We became close. Before he passed, he had asked me to maintain his renowned DFO solvers, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. These solvers are standard benchmarks in the DFO community, and they are widely used by scientists and engineers.

    However, Professor Powell implemented these solvers in Fortran 77, with the unique coding style mentioned here a few times by others. For most of us who lack the genius of Professor Powell, the code is nontrivial to understand or maintain, let alone extend. For many practitioners, this has become an obstacle to exploiting these solvers in their applications. Even worse, it has hindered researchers from exploring the wealth left by Professor Powell to us. Therefore, starting July 2020, I have been devoting a major part of my time on developing PRIMA ( ), a package that aims to provide the modernized reference implementation for Powell's DFO solvers. This is a project similar to the translation, interpretation, and annotation of Euclid’s Elements. It will make Powell's solvers easily understandable to everyone, not only the experts. Few people remember who translated Elements, but it is a job that must be done.

    I met Professor Powell for the last time in San Diego during SIAM Optimization Conference 2014. He came to listen to my talk -- the last talk in the last parallel session. It was a tremendous honour for me. I still remember vividly the question he asked, and the chat we had after the talk. Later that year, I invited him to join the DFO stream that I would co-chair at the 2015 International Conference on Continuous Optimization (ICCOPT 2015), but he responded that he would probably not be there. I did not realize what he really meant until I heard from him again in April 2015, when he asked me to take care of his DFO solvers after he passed.

    I will miss Professor Powell forever. PRIMA, on which I have spent more than three years day to day almost full time, summing up to 10,000+ hours, is dedicated to my deep memory of him.