Mathematics

Modern variational analysis can be viewed as a certain outgrowth of the classical calculus of variations, optimal control and mathematical programming, where perturbation/approximation methods and stability/sensitivity issues play a crucial role. In this talk we discuss recent advances in variational analysis and its applications in dynamic optimization models governed by nonconvex differential inclusions in both finite and infinite dimensions, which happen to be a natural framework for the unifying study of various problems in the calculus of variations and optimal control. We discuss an approach to such problems based on finite-difference/discrete approximations of differential systems and thus related to both numerical and theoretical issues in optimization and control. Developing this approach, we reduce continuous-time optimal control problems to sequences of constrained mathematical programs of a special type, which are comprehensively studied by using modern methods of variational analysis and generalized differentiation. The main results justify well-posedness/stability of discrete approximations and establish necessary optimality conditions of Euler-Lagrange and Weierstrass-Pontryagin types for nonconvex differential inclusions employing advanced tools of variational analysis.