Many inverse problems for differential equations
can be formulated as optimal control problems.
It is well known that inverse problems often need to
be regularized to obtain good approximations.
This work presents a systematic method to regularize
and to establish error estimates for approximations to
some control problems in high dimension,
based on symplectic approximation
of the Hamiltonian system for the control problem. In particular
the work derives error estimates
and constructs regularizations...
The powerful Hamilton-Jacobi theory is used for constructing regularizations and error estimates for optimal design problems. The constructed Pontryagin method is a simple and general method for optimal design and reconstruction: the first, analytical, step is to regularize the hamiltonian; next the solution to its stationary hamiltonian system, a nonlinear partial differential equation, is computed with the Newton method. The method is efficient for designs where the hamiltonian function can be...
The powerful Hamilton-Jacobi theory is used for
constructing regularizations and error estimates for optimal design
problems. The constructed Pontryagin method is a simple and general
method for optimal design and reconstruction: the first, analytical,
step is to regularize the Hamiltonian; next the solution to its
stationary Hamiltonian system, a nonlinear partial differential
equation, is computed with the Newton method. The method is
efficient for designs where the Hamiltonian function...
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