Hamilton-Jacobi Theory and Parametric Analysis in Fully Convex Problems of Optimal Control
نویسنده
چکیده
For optimal control problems satisfying convexity conditions in the state as well as the velocity, the optimal value is studied as a function of the time horizon and other parameters. Conditions are identified in which this optimal value function is locally Lipschitz continuous and semidifferentiable, or even differentiable. The Hamilton-Jacobi theory for such control problems provides the framework in which the results are obtained.
منابع مشابه
Envelope representations in Hamilton-Jacobi theory for fully convex problems of control
This paper is a sequel to the one in this same session which surveys recent results on the role of convexity in Hamilton-Jacobi theory. We describe here how value functions in optimal control can be represented as upper and lower envelopes involving so-called kernel functions. Particularly noteworthy is a lower envelope formula given in terms of the dualizing kernel, which is a value function i...
متن کاملConvexity in Hamilton-Jacobi Theory II: Envelope Representations
Upper and lower envelope representations are developed for value functions associated with problems of optimal control and the calculus of variations that are fully convex, in the sense of exhibiting convexity in both the state and the velocity. Such convexity is used in dualizing the upper envelope representations to get the lower ones, which have advantages not previously perceived in such ge...
متن کاملA Transformation Method for Solving the Hamilton{--}jacobi{--}bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem
We propose and analyse a method based on the Riccati transformation for solving the evolutionary Hamilton–Jacobi–Bellman equation arising from the dynamic stochastic optimal allocation problem. We show how the fully nonlinear Hamilton–Jacobi– Bellman equation can be transformed into a quasilinear parabolic equation whose diffusion function is obtained as the value function of a certain parametr...
متن کاملDuality and dynamics in Hamilton-Jacobi theory for fully convex problems of control
This paper describes some recent results in HamiltonJacobi theory that hold under strong convexity assumptions on the data. Generalizations of linearquadratic control models satisfy such assumptions, for example. The results include a global method of characteristics and a strong duality theory.
متن کاملDetermining the Optimal Control When Numerically Solving Hamilton-Jacobi-Bellman PDEs in Finance
Numerous financial problems can be posed as nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In order to guarantee that the discretized equations converge to the viscosity solution, the required conditions are pointwise consistency, l∞ stability, and monotonicity. We use the positive coefficient method, choosing central differencing as much as possible, to construc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Global Optimization
دوره 28 شماره
صفحات -
تاریخ انتشار 2004