Obituaries: Jack Warga

March 18, 2012

Jack Warga, 1922–2011
Jack Warga, a highly regarded Polish–American applied mathematician, was a professor of mathematics at Northeastern University from 1966 until his retirement in July 1993. He worked in the aerospace industry before moving to Northeastern; he held a Weizmann Memorial Fellowship at the Weizmann Institute of Science in Rehovot, Israel, in 1956 and 1957, and spent a sabbatical year there in 1973. Dur-ing 1981 he was on sabbatical leave at Tel Aviv University.

Jack (originally Yitzhak) was born into a Jewish family in Warsaw; his father was a furrier, and the family lived on Bielanska Street, in the city center. Unlike many families in the Jewish community, they spoke Polish rather than Yiddish at home. Yitzhak studied at a Polish school, where he became deeply interested in the Polish language and literature, especially poetry. While in school, he belonged to a socialist youth organization, and it was there, as he wrote in his memoirs, that he acquired his idealistic approach to life. In later life, he retained a very good literary Polish, if a bit old-fashioned.

In the late 1930s, in the face of growing anti-Semitism and hooligan attacks, his parents sent him to Brussels, where relatives were living, for further studies. This probably saved his life. His mother and younger brother perished in the Holocaust; his father survived, sheltered by a Polish friend. Yitzhak was a brilliant student, but his education in Brussels was interrupted by the German invasion of Belgium. He escaped to Vichy France and later managed to emigrate to the United States via Spain and Cuba.

After the war Jack resumed his education in the U.S., which culminated in a PhD in mathematics from New York University in 1950. Working initially in industry, he was by 1966 manager of the mathematics department in the R&D division of the aerospace corporation Avco. The mathematical problems that he encountered during this period inspired his interest in optimization and control theory, to which he made seminal contributions. The most notable are presented in a landmark two-part 1962 paper in the Journal of Mathematical Analy-sis and Applications, in which he introduced the notion of relaxed controls, proved their existence for a broad class of optimal control problems, and derived necessary conditions for a relaxed control to be optimal.

Jack maintained his career-long interest in relaxation and optimality through studies in a variety of contexts. His pioneering work on these themes is the subject of his classic monograph Optimal Control of Differential and Functional Equations (Academic Press, 1972; translated into Russian, 1977). Although this work was fairly abstract, Jack asserted that his experiences in industry had profoundly influenced his research; he was most comfortable working on problems with a clear connection to an application area, which opened the way for intuition and mathematical analysis.

A keen interest in nonsmooth control systems led to Jack's formulation, in 1975, of new generalized derivatives for nonsmooth functions, now referred to as "Warga's derivate containers." Concepts of generalized derivatives emerging around this time, including Warga's derivate containers, played a crucial role in the subsequent development of optimal control and optimization, in which nonsmoothness has had a dominant role. Other areas to which Jack made important contributions include controllability conditions, higher-order optimality conditions, numerical methods, optimality conditions for optimal control problems with state constraints, time delays, and with min–max costs, and differential games.

Alex Ioffe recalls his first exposure to Jack's research, at the 1966 International Congress of Mathematicians in Moscow. Alex, after presenting a short communication on the subject of relaxation, was taken completely by surprise when A. Arkin asked whether he was acquainted with the work of Warga. A subsequent exchange of preprints with Jack initiated a lasting academic communication. This was not at all straightforward, especially when Alex became a "refusenik." Throughout that time, Jack offered Alex both support and assistance in publishing his research. Among Alex's souvenirs is a disk of a January 1987 interview by Jack and Loren Graham on Boston public TV during the hunger strike Alex conducted to protest his son's detention in the Soviet Union. Jack's unfailing support continued as Alex and his family subsequently adjusted to life in the West.

Jack was highly principled with regard to both his professional and personal conduct. As the managing editor of SIAM Journal on Control and Optimization, he used his considerable influence to put a stamp of integrity and fair dealing on the emerging optimal control theory community during its heyday in the 1960s and 70s. In common with other original thinkers, he was not interested in a close reading of other people's work; he made his own judgments about what the important problem areas were and worked everything out in his own way, from first principles. He eschewed self-promotion: His style was to write papers devoid of extravagant claims and let the results speak for themselves.

Jack's many friends and colleagues remember him as an exceptional human being. His kindness, generosity, and patience, particularly toward the young researchers he inspired and guided, are legendary. Boris Mordukhovich refers to the many people whom Jack generously helped, not expecting anything in return. He encouraged young mathematicians (including those who were not his students), advising them to write papers and publish them. Boris recalls meeting Jack three days after arriving in the United States: "He helped me enormously by advising me on the preparation of my CV and introducing me to the mathematical community. He even bought me shoes after seeing that I was poorly dressed." Helene Frankowska remembers how, in the early 1980s, when she was pursuing her PhD studies at SISSA, separated from her advisers and academically isolated, she had initiated a correspondence with Jack over their shared interests in nonsmooth analysis. Then, and subsequently, he provided valuable comments about her work. He would later invite her to stay at his home in Boston.

Jack's sensitivity to the needs of emerging researchers is exemplified by his work with his PhD student Jim Zhu, for whom Jack set the problem of seeking necessary conditions of optimality for variational problems involving non-commensurate time delays. (Jack had already dealt himself with the simpler case of commensurate delays.) Jim describes Jack's encouraging him to work on his own, without paying too much attention to other people's methods. Jack attentively followed the work done by Jim over several months, in which he provided a solution combining chaotic dynamical systems theory and Jack's earlier relaxation methods. Jack then encouraged Jim to publish the findings on his own. Two years later, Jack further generalized the results to cover a much larger class of non-commensurate delays, using a totally different approach, based on approximation methods that he was familiar with all the time. To give his student the freedom to explore, acquire independence, and come up with his own techniques, Jim realized later, Jack had held back in solving the problem himself.

The sad news of Jack's death on June 26, 2011, soon after a fall, came as a shock to his many friends and colleagues. He was survived by a son, Arthur, a daughter, Charna, and their families. Arthur died in August 2011, after a prolonged illness.

The members, current and past, of the editorial board of SIAM Journal on Control and Optimization have fond memories of Jack, who played a very active role on the editorial board of the journal from 1964 to 1989, serving as co-managing editor (with Lucien Neustadt) and then managing editor from 1967 through 1978. Jack's integrity and high standard of scholarship helped shape the journal into an influential forum for researchers in the area of control theory and optimization.---The editorial board of SICON organized this article in memory of Jack by contacting many of his colleagues and friends. They are indebted to Kazimierz Malanowski for providing details of Jack's early history. An extended tribute will be circulated separately by contributors to this article, who hope that the spirit of their great colleague and pioneer will live on.

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