Obituary: Asen L. Dontchev

By Vladimir M. Veliov, George Yin, and Michael P. Polis

Asen L. Dontchev, an internationally renowned mathematician in the fields of variational analysis, optimization, and optimal control, passed away on September 16, 2021, after battling cancer. He was 73 years old.

Asen was born on June 19, 1948, in Pleven, Bulgaria, where he completed his high school education. Recognition of his mathematical talent inspired him to study at the Warsaw University of Technology; he completed his Ph.D. in control sciences in 1974. Upon returning to Bulgaria, Asen joined the Bulgarian Academy of Sciences’ Institute of Mathematics and Mechanics (now the Institute of Mathematics and Informatics). He became a full professor in 1987. During this period, Asen published his first book: Perturbations, Approximations, and Sensitivity Analysis of Optimal Control Systems [1].

In 1989, Asen accepted a visiting professor position at the University of Florida. He became an adjunct professor at the University of Michigan in 2000 and served as program director of the Analysis Program in the National Science Foundation’s Division of Mathematical Sciences from 2007 to 2009.

During his distinguished research career, Asen made substantial contributions to several areas of analysis and optimization; these contributions are evident in his 128 papers and six books. He wrote his last book [2]—to be published post mortem—while knowing that he had a terminal illness. This book, titled Lectures on Variational Analysis, will be the first tutorial on variational analysis that focuses on optimization.

In the early part of his career, Asen’s research focused on sensitivity analysis and error analysis of approximations of optimal control problems with various kinds of constraints. His series of works on singular perturbations in optimal control led to the new and very influential understanding that the limit problem must be appropriately defined and may differ from the one that is obtained by a formal order reduction (as in the fundamental Tikhonov theorem). Asen’s investigations in this period resulted in a book with Tullio Zolezzi entitled Well-Posed Optimization Problems [4].

Asen continued to develop rich new ideas after moving to the U.S. A fundamental paper with William W. Hager about Lipschitzian stability in nonlinear control and optimization provided a powerful machinery for analysis of the stability properties of generalized equations (e.g., those that represent necessary optimality conditions). This machinery and the underlying ideas have made a substantial impact on the optimization community and resulted in numerous contributions by Asen—some with coauthors—on the stability and error analysis of discrete approximations in optimal control. 

Asen’s works on inverse mappings and implicit function theorems for set-valued mappings are also worth mentioning. His collaboration with Terry Rockafellar on fundamental questions of variational analysis was especially productive and culminated in the book Implicit Functions and Solution Mappings: A View from Variational Analysis [3], which explored various regularity properties of set-valued mappings, implicit function theorems, the radius of preservation of regularity under disturbances, and applications in numerical analysis. The abstract notion of metric subregularity—introduced by Asen and Rockafellar in 2004 and systematically investigated by Asen and subsequent collaborators—became a powerful tool in approximation theory for optimization problems. Asen used this theoretical foundation when he devoted a part of his final years to justification and improvements of model predictive control, a main tool for process control in industry, aerospace engineering, and power electronics.

Asen provided outstanding services to the scientific community and made substantial contributions. He served on the editorial boards of numerous important journals, including the SIAM Journal on Optimization, SIAM Journal on Control and Optimization (SICON), Computational Optimization and Applications, Journal of Mathematical Analysis and Applications, Journal of Optimization Theory and Applications, Journal of Dynamical and Control Systems, Open Applied Mathematics Journal, and Journal of Industrial and Management Optimization, among others. He was also an associate editor of Mathematical Reviews for nearly 30 years.

Asen’s passing is a great loss to SIAM, particularly to SICON. He served as a corresponding editor for SICON since 2015 and was previously an associate editor from 2000 to 2014. “Editorial Board service of this length is impressive and not often seen,” Mitch Chernoff, the Publications Manager at SIAM, said. 

After Asen’s death, many individuals on the SICON Editorial Board reflected on their memories of him. “Asen was extremely knowledgeable and responsive,” Jinglai Shen said. “He was also very supportive to junior editors. He always provided timely and insightful suggestions and supported my ideas when I had a difficult time making a decision on a paper and had to consult him. It was such a pleasant experience working with Asen — I learned a lot from him.” Even in his final moments, Asen kept the scientific community among his top priorities. Shortly before his passing, he suggested that SICON find a replacement for himself as the corresponding editor to facilitate continuity and a smooth editorial transition.

Throughout his career, Asen mentored several generations of mathematicians. He was an excellent lecturer and possessed a remarkable ability to disseminate his knowledge and inspire young researchers. Due to his openness and friendliness, he had a large number of scientific contacts in universities all over the world and partnered with more than 60 coauthors.

Asen loved the outdoors and was an avid fisherman. He was happiest and most relaxed on the water in his boat. He was extremely proud of his children and was an enthusiastic grandfather.

Asen is survived by his wife Dora, daughter Mira, son Kiko, and three grandchildren. He had many friends, mentees, and collaborators and will be deeply missed by everyone who knew him.

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References
[1] Dontchev, A.L. (1983). Perturbations, approximations and sensitivity analysis of optimal control systems. In Lecture notes in control and information sciences (Vol. 52). Berlin: Springer-Verlag.
[2] Dontchev, A.L. (to appear). Lectures on variational analysis. New York, NY: Springer.
[3] Dontchev, A.L., & Rockafellar, R.T. (2014). Implicit functions and solution mappings: A view from variational analysis (2nd Ed.). New York, NY: Springer.
[4] Dontchev, A.L., & Zolezzi, T. (1993). Well-posed optimization problems. New York, NY: Springer.

Vladimir M. Veliov is a professor of operations research and control systems at the Vienna University of Technology. George Yin is a professor of mathematics at the University of Connecticut. Michael P. Polis is an emeritus professor of engineering at Oakland University.