Structure of approximate solutions of variational problems with extended-valued convex integrands

In Section 4 we show the convexity of the minima of (2) in finite dimension, and in Section 5 we investigate the convexity of the minimizers in the infinite dimensional Wiener space..

Receding horizon control, model predictive control, value function, optimality systems, Riccati equation, turnpike property.. AMS

In the case when F is continuous, the characterization given in the above theorem amounts saying that the value function is the only lsc solution of the HJB equation

Zaslavski, The turnpike property for extremals of nonautonomous variational problems with vector-valued functions, Nonlinear Anal. Zaslavski, Turnpike Properties in the Calculus

For the first class of integrands we show the existence of a minimizing sequence of Lipschitzian functions while for the second class we establish that an infimum on the full

ZASLAVSKI, The existence and structure of extremals for a class of second order infinite horizon variational problems, J. ZASLAVSKI, Structure of extremals for

Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods we get

Using the existence and uniqueness of the solution to particular elliptic variational inequality, we consider a family of distributed optimal control problems on the internal energy