Moment problems are ubiquitous throughout engineering and science and have had a profound impact on the development of modern mathematical analysis. Power moments of probability measures play an important role in statistical modeling and in its application to information theory, communications, signals and systems. Applications of the trigonometric moment problem to systems and control also have a long and fruitful history, including the rational covariance extension problem. Analytic interpolation problems are an important class of moment problems with applications to circuit theory, power systems, robust control, signal processing, spectral estimation, model reduction, and stochastic realization theory. A common feature arising in many engineering applications is that the desired solution needs to be a rational positive measure of a bounded degree, reflecting its implementability by a finite dimensional device. These moment problems are typically underdetermined and give rise to families of particular solutions, and finding a solution that also satisfies a natural optimality criterion or design specification is an important general problem. While this nonclassical version of the moment problem is decidedly nonlinear, there exists a natural, universal family of strictly convex optimization criteria defined on the convex set of particular solutions. Taking a global-analysis approach, where one studies the family of solutions as a whole, provides a powerful paradigm for smoothly parameterizing, comparing and shaping the solutions based on various additional design criteria. It also enables us to establish the smooth dependence of solutions on problem data, thereby facilitating tuning of solutions. It also provides a generalization of the generalized interpolation results of Sarason.

Anders Lindquist is a foreign Academician of the Chinese Academy of Sciences and a Zhiyuan Chair Professor at Shanghai Jiao Tong University. He is also an Emeritus Professor at the Royal Institute of Technology (KTH), Stockholm, Sweden. After receiving a PhD from KTH, he had a full academic career from Assistant to Full Professor in the United States. After this he was appointed to the Chair of Optimization and Systems Theory at KTH, where he also served as the Director of the Center for Industrial and Applied Mathematics. For ten years he was also the Head of the Mathematics Department there. Lindquist is also a Member of the Royal Swedish Academy of Engineering Sciences, a foreign Member of the Russian Academy of Natural Sciences, an Honorary Member the Hungarian Operations Research Society, a Life Fellow of IEEE, a Fellow of SIAM, and a Fellow of IFAC. He is an honorary doctor at the Technion, Israel, and the recipient of the 2009 Reid Prize in Mathematics from SIAM and of the 2003 Axel by Outstanding Paper Award from the IEEE Control System Society. He is also an Honorary Professor at the China University of Petroleum, Qingdao.