Control Theoretic Splines with Constraints

It is well known that the interpolating cubic spline can be viewed as a solution of the double integrator linear-quadratic problem. This fascinating connection between the classical approximation theory and the theory of optimal control has been discovered by researches from both sides in different times and often independently. In this talk I will review some developments on control theoretic splines with constraints, such as convexity and restricted range, and show how to handle the constraints both theoretically and numerically.

Dr. Dontchev is currently employed by Mathematical Reviews, a division of the American Mathematical Society. He is also affiliated with the University of Michigan and the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences. His research interests are centered around estimating the effect of perturbations and approximations on solutions of variational problems, in particular problems in the general areas of optimization, optimal control, calculus of variations and approximation theory. His interest is also in problems with constraints where tools from classical analysis cannot be applied. For more specific information about his current research interests, please see his recent book coauthored with R.T. Rockafellar, “Implicit Functions and Solution Mappings, A View from Variational Analysis,” which appeared in Springer Monographs in Mathematics in 2009.